| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{n}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a {y^{\prime \prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a {y^{\prime \prime }}^{n}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}&=1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}&=x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{3}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}+y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+{y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 15 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}+y^{\prime }&=1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 17 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 18 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 19 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}+y^{\prime }&=x \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 20 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+{y^{\prime }}^{2}&=x \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 21 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 22 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}+y^{\prime }+y&=0 \end {array} \] |
✗ |
✗ |
✗ |
✗ |
|
| 23 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+{y^{\prime }}^{2}+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 25 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 26 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=x +1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 27 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=x^{2}+x +1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 28 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=x^{3}+x^{2}+x +1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 29 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 30 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\cos \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 31 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 32 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 33 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=x +1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 34 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=x^{2}+x +1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 35 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=x^{3}+x^{2}+x +1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 36 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=\sin \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 37 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=\cos \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 38 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 39 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 40 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x +1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 41 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x^{2}+x +1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 42 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x^{3}+x^{2}+x +1 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 43 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 44 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\cos \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 45 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime \prime }}^{2}+y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 46 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 47 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {y^{\prime \prime }}^{2}+y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 48 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 49 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3} {y^{\prime \prime }}^{2}+y y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 50 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+y y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 51 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime \prime }}^{3}+y^{3} y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 52 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y {y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y^{2} {y^{\prime }}^{2}&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2}&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } y^{\prime \prime }+y^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } y^{\prime \prime }+y^{n}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (x +y\right )^{4} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (y^{2}+3\right ) {y^{\prime }}^{2}&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )}&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 15 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {2 y}{x^{2}}&=x \,{\mathrm e}^{-\sqrt {x}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=x \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 17 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 18 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-c^{2} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 19 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 20 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=2 x^{3}-x^{2} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 21 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 22 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \end {array} \] |
✗ |
✓ |
✗ |
✗ |
|
| 23 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=8 x^{3} \sin \left (x \right )^{2} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 25 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=x^{5} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 25 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 \cos \left (x \right )^{3} y&=2 \cos \left (x \right )^{5} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 26 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}&=4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 27 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x^{m +1} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 28 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 29 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 30 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 31 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y&=x \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 32 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y&={\mathrm e}^{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 33 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&={\mathrm e}^{x^{2}} \sec \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 34 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 \left (x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 35 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 36 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}&=0 \end {array} \] |
✗ |
✓ |
✗ |
✗ |
|
| 37 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 38 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 39 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y \cot \left (x \right )&=2 \cos \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 40 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 41 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x -y^{2} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 42 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x} \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 43 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 44 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 45 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 46 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 47 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y x&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 48 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{{1}/{3}}\\ y \left (0\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 49 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=3 x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right )\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|