| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }+x y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime \prime }-2 x y^{\prime }+10 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{2} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 15 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 16 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 17 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 18 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 19 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 20 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 21 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 22 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+x y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 23 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 25 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 26 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 27 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 28 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 29 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 31 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 32 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 33 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 34 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (3+2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 35 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 36 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 38 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 39 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 40 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 41 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 42 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 43 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 44 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 45 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (3+2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 46 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 47 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2\right ) y^{\prime \prime }+x y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 48 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 49 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 50 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 51 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 52 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 53 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 54 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 55 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 56 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 57 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 58 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 59 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 60 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 61 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 62 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 63 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 64 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 65 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 66 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 67 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 68 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 69 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 70 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 71 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 72 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 73 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 74 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 75 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 76 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 77 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (-x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 78 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 79 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 80 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 81 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 82 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 83 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 84 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 85 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 86 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 87 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 88 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 89 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 90 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 91 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 92 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 93 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 94 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 95 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 96 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 97 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 98 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 99 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 100 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 101 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 102 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 103 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 104 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 105 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 106 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 107 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 108 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 109 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 110 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 111 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 112 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 113 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 114 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 115 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 116 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 117 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 118 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 119 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 120 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 121 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 122 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 123 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 124 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 125 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 126 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 127 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 128 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 129 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 130 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 131 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 132 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 133 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (-9 x +1\right ) y^{\prime }+\left (1-70 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 134 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 135 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 136 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 137 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 138 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 139 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 140 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 141 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 142 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 143 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 144 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 145 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 146 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 147 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 148 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 149 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 150 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 151 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 152 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 153 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 154 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 155 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 156 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 157 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 158 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 159 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 160 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 161 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 162 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 163 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (3+2 x \right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 164 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 165 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 166 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 167 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 168 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 169 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 170 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 171 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (-9 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 172 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 173 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 174 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 175 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 176 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 177 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 178 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 179 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 180 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 181 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 182 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 183 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 184 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 185 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 186 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 187 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 188 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 189 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 190 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 191 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 192 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 193 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 194 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 195 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 196 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 197 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 198 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 199 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 200 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 201 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 202 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 204 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 205 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 206 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 207 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 208 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 209 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+y t&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 210 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 211 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 212 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 213 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 214 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 215 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 216 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 217 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 218 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 219 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 220 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 221 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 222 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 x y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 223 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 224 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 225 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 226 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 227 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 228 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 229 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+x y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 230 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 231 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x y^{\prime \prime }-x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 232 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 233 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 234 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 235 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 236 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 237 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 238 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 239 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 240 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 241 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 242 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 243 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 244 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 245 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 246 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 247 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 248 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 249 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 250 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 251 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 252 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 253 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 254 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 255 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 256 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 257 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 258 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 259 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 260 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 261 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 262 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 263 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 264 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 265 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {x y^{\prime }}{2}-\frac {3 y x}{4}&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 266 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 267 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 268 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 269 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 270 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 271 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 272 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 273 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 274 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 275 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 276 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 277 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 278 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 279 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 280 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a^{2} y+y^{\prime \prime }&=\frac {6 y}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 281 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 282 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 283 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 284 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 285 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 286 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 287 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 288 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 289 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 290 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 291 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 292 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 293 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 294 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 295 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 296 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 297 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 298 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 299 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 300 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+x y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 301 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x -1\right )^{2} y^{\prime \prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 302 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 x y^{\prime }+x^{2} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 303 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 304 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (x y^{\prime }-y\right )&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 305 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 306 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 307 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 309 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 x y^{\prime }+8 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 310 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 311 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 313 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 314 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 315 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 316 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 317 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 318 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 319 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 320 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 321 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 322 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 325 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 326 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 327 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }-\left (3+2 x \right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 328 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 329 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 330 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 331 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (-6+x \right ) y^{\prime }-3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 332 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+\lambda y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 333 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 334 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 335 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 336 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+3 y^{\prime }+x^{3} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 337 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 338 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 339 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 340 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 341 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 342 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 343 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 344 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 345 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 346 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 347 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 348 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 349 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 350 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 351 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 352 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 353 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 354 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 355 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 356 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 357 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4}&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 358 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 359 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 360 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 361 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 362 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 363 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 364 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 365 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {u}{x^{2}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 366 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 367 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 368 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 369 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 370 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y}{2 x^{4}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 371 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 372 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 373 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 374 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 375 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 376 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 377 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 378 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 379 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 380 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 381 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 382 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 383 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 384 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 385 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 388 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 389 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 390 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 391 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 392 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 394 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 395 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 396 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 398 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left (x^{2}+3\right ) y \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 399 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 400 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 401 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 402 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 404 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 405 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 406 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 407 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 408 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 409 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 410 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 411 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 412 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 413 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 414 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }+x y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 415 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime \prime }-2 x y^{\prime }+10 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 416 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 417 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 418 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 419 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 420 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 421 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 422 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 423 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 424 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 425 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 426 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 427 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 428 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 429 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 430 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 431 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 432 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 433 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 434 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 435 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+x y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 436 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 437 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 438 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 439 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 440 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 441 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 442 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 444 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 445 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (3+2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 446 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 447 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 448 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 449 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 450 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 451 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 452 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 453 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (3+2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 454 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 455 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 456 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 457 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 458 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 460 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 461 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 462 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 463 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 464 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 465 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 466 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 467 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 468 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (3+2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 469 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 470 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 472 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 473 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 474 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 475 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 476 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 477 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 478 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 479 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (3+2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 480 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 481 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2\right ) y^{\prime \prime }+x y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 482 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 483 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 484 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 485 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 486 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 487 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 488 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 489 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 490 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 491 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 492 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 493 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 495 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 496 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 497 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 498 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 499 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 500 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 501 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 502 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 503 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 504 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 505 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 506 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 507 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 508 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 509 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 510 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 511 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (-x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 512 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 513 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 514 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 515 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 516 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 517 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 518 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 519 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 520 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 521 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 522 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 523 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 524 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 525 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 526 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 527 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 528 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 529 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 530 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 531 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 532 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 533 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 534 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 535 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 536 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 537 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 538 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 539 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 540 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 541 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 542 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 543 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 544 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 545 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 546 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 547 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 548 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 549 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 550 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 551 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 552 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 553 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 554 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 555 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 556 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 557 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 558 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 559 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 560 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 561 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 562 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 563 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 564 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 565 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 566 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 567 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (-9 x +1\right ) y^{\prime }+\left (1-70 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 568 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 569 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 570 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 571 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 572 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 573 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 574 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 575 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 576 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 577 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 578 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 579 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 580 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 581 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 582 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 583 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 584 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 585 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 586 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 587 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 588 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 589 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 590 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 591 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 592 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 593 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 594 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 595 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 596 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 597 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (3+2 x \right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 598 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 599 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 600 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 601 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 602 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 603 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 604 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 605 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (-9 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 606 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 607 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 608 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 609 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 610 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 611 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 612 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 613 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 614 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 615 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 616 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 617 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 618 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 619 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 620 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 621 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 622 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 623 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 624 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 625 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 626 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 627 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 628 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 629 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 630 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 631 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 632 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 633 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 634 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 635 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 636 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 638 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 639 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 640 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 641 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 642 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 643 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+y t&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 644 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 645 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 646 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 647 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 648 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 649 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 650 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 651 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 652 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 653 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 654 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 655 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 656 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 657 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 658 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 659 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 660 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 661 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 x y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 662 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 663 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 664 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 665 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 666 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 667 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 668 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+x y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 669 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 670 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x y^{\prime \prime }-x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 671 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 672 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 673 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 674 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 675 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 676 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 677 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 678 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 679 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 680 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 681 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 682 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 683 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 684 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 685 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 686 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 687 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 688 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 689 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 690 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 691 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 692 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 693 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 694 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 695 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 696 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 697 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 698 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 699 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 700 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 701 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 702 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 703 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 704 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 y x}{16}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 705 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 706 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 707 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 708 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 709 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 710 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 711 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 712 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 713 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 714 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 715 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 716 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 717 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 718 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 719 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a^{2} y+y^{\prime \prime }&=\frac {6 y}{x^{2}} \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 720 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 721 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 722 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 723 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 724 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 725 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 726 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x +2\right ) x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 727 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 728 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 729 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 730 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 731 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 732 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 733 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 734 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 735 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 736 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 737 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 738 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 739 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 740 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 741 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 742 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 743 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 744 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+x y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 745 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x -1\right )^{2} y^{\prime \prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 746 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 x y^{\prime }+x^{2} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 747 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 748 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (x y^{\prime }-y\right )&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 749 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 750 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 751 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 754 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 755 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 757 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 758 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 759 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 760 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 761 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 762 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 763 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 764 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 765 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 766 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 769 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 770 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 771 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }-\left (3+2 x \right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 772 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 773 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 774 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 775 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (-6+x \right ) y^{\prime }-3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 776 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+\lambda y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 777 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 778 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 779 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 780 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+3 y^{\prime }+x^{3} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 781 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 782 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 783 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 784 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 785 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 786 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 787 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 788 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 789 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 790 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 791 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 792 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 793 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 794 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 795 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 796 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 797 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 798 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 799 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 800 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 801 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 802 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 803 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 804 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 805 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 806 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 807 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 808 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 809 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+2 u^{\prime }+u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 810 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 811 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 812 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 813 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 815 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 816 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 817 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 818 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 819 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 820 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 821 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 822 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 823 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 824 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 825 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 826 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 827 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 828 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 829 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 830 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 831 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 832 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 833 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 834 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 835 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 836 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 837 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 838 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left (x^{2}+3\right ) y \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 839 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 840 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 841 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 843 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 844 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {2 y}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 845 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {6 y}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 x \left (x -1\right )}\right ) y \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {20 y}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {12 y}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y}{4 x^{2}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y}{x^{2}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Kovacic 1985 paper. page 13. section 3.2, example 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| Kovacic 1985 paper. page 14. section 3.2, example 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left (\frac {6}{x^{2}}-1\right ) y \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| Kovacic 1985 paper. page 15. Weber equation |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| Kovacic 1985 paper. page 19. section 4.2. Example 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| Kovacic 1985 paper. page 23. section 5.2. Example 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 x \left (x -1\right )}\right ) y \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| Kovacic 1985 paper. page 25. section 5.2. Example 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| Kovacic 2005 paper. Example 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {y}{4 x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| David Saunders 1981 paper. Example 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left (x^{2}+3\right ) y \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| David Saunders 1981 paper. Example 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }&=2 y \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 1 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|