| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\cos \left (y\right ) \sec \left (x \right )}{x} \end {array} \] |
✓ |
✓ |
✓ |
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| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \left (\cos \left (y\right )+y\right ) \end {array} \] |
✓ |
✓ |
✓ |
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| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x} \end {array} \] |
✓ |
✓ |
✓ |
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| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y+1 \end {array} \] |
✓ |
✓ |
✓ |
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| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x +1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+\frac {\sec \left (x \right )}{x} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x +\frac {\sec \left (x \right ) y}{x} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {2 y}{x}\\ y \left (0\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {2 y}{x} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 15 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{x} \end {array} \] |
✓ |
✓ |
✓ |
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| 16 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {-y x -1}{4 x^{3} y-2 x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 17 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {{y^{\prime }}^{2}}{4}-x y^{\prime }+y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 18 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {\frac {y+1}{y^{2}}}\\ y \left (0\right )&=1\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 19 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \end {array} \] |
✗ |
✗ |
✗ |
✗ |
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| 20 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {y}{3}&=\frac {\left (1-2 x \right ) y^{4}}{3} \end {array} \] | ✓ | ✓ | ✓ | ✓ |
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| 21 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {y}+x \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 23 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=x y^{\prime }+{y^{\prime }}^{2} x^{2} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 25 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right ) y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 26 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 27 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y^{\prime }}{x +y}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 28 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y^{\prime }}{x}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 29 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 30 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 31 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {5 x^{2}-y x +y^{2}}{x^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 32 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t +3 x+\left (x+2\right ) x^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 33 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{1-y}\\ y \left (0\right )&=2\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 34 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} p^{\prime }&=a p-b p^{2}\\ p \left (\operatorname {t0} \right )&=\operatorname {p0}\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 35 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\frac {2}{x}+2 x y y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 36 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f^{\prime } x -f&=\frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 37 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }-2 y+b y^{2}&=c \,x^{4} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 38 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }-y+y^{2}&=x^{{2}/{3}} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 39 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime }+u^{2}&=\frac {1}{x^{{4}/{5}}} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 40 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }-y&=x \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 41 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }+y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 41 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime \prime }+2 y^{\prime }+4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 42 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+4 y&=1 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
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| 43 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+4 y&=\sin \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 44 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&={y^{\prime }}^{2} x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 45 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }&=1-x {y^{\prime }}^{3} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 46 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f^{\prime }&=\frac {1}{f} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 47 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+4 y^{\prime }&=t^{2} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 48 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime }&=0\\ y \left (3\right )&=2 \pi \\ y^{\prime }\left (3\right )&={\frac {2}{3}}\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 49 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 50 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 51 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 52 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}}&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
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| 53 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 54 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 55 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 56 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=f \left (t \right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 57 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=k \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 58 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-4 \sin \left (x -y\right )-4 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 59 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\sin \left (x -y\right )&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 60 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=4 \sin \left (x \right )-4 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 61 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 62 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }&=1 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 63 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }&=x \end {array} \] |
✗ |
✗ |
✗ |
✗ |
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| 64 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime \prime }&=x \end {array} \] | ✗ | ✓ | ✗ | ✗ |
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| 65 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime \prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 66 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y y^{\prime \prime }&=\sin \left (x \right ) \end {array} \] |
✗ |
✗ |
✗ |
✗ |
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| 67 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y y^{\prime \prime }+y&=5 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 68 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y y^{\prime \prime }+b y&=c \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 69 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y^{2} y^{\prime \prime }+b y^{2}&=c \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 70 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y y^{\prime \prime }+b y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 71 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=9 x \left (t \right )+4 y \left (t \right )\\ y^{\prime }\left (t \right )&=-6 x \left (t \right )-y \left (t \right )\\ z^{\prime }\left (t \right )&=6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 72 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=x \left (t \right )-3 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x \left (t \right )+7 y \left (t \right )\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 73 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+5 y \left (t \right )\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 74 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=7 x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=-4 x \left (t \right )+3 y \left (t \right )\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 75 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=y \left (t \right )\\ z^{\prime }\left (t \right )&=z \left (t \right )\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 76 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=2 x \left (t \right )+y \left (t \right )-z \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )+2 z \left (t \right )\\ z^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )+4 z \left (t \right )\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 77 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 78 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}&=-x \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 78 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}&=-x\\ y \left (0\right )&=3\\ \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 79 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 80 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2}+y^{2} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 81 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 \sqrt {y}\\ y \left (0\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 82 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 83 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {1-y^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 84 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2}+y^{2}-1 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 85 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 y \left (x \sqrt {y}-1\right )\\ y \left (0\right )&=1\\ \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 86 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 87 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=0\\ y \left (0\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 88 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 88 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=0\\ y^{\prime }\left (0\right )&=0\\ y \left (0\right )&=1\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 89 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y y^{\prime }&=2 x \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 90 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y^{2}-x -x^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -2 x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -3 x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -x^{2}-x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -x^{3}+2&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -x^{4}-6&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -x^{5}+24&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -x^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -x^{3}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a x y^{\prime }-b x y-c x&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2}&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a x y^{\prime }-b x y-x^{3} c&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 15 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 16 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 16 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 17 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-y x -x^{2}-2&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 18 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }-y x -x^{2}-4&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 19 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{3}+1&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 20 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-y x -x^{3}-x^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 21 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{3}+2&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 22 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-y x -x^{3}+2&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 23 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }-y x -x^{3}+2&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }-y x -x^{3}+2&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 25 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-8 y^{\prime }-y x -x^{3}+2&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 26 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{4}+3&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 27 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{3}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 28 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y x -x^{3}+2&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 29 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y x -x^{6}+64&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 30 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y x -x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 31 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y x -x^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 32 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y x -x^{3}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 33 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y x -x^{6}-x^{3}+42&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 34 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y-x^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 35 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y-x^{3}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 36 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y-x^{4}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 37 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y-x^{4}+2&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 38 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 x^{2} y-x^{4}+1&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 39 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{3} y-x^{3}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 40 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{3} y-x^{4}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 41 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2}&=0 \end {array} \] | ✗ | ✓ | ✗ | ✗ |
|
| 42 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3}&=0 \end {array} \] |
✗ |
✗ |
✗ |
✗ |
|
| 43 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime }-y x -x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 44 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y^{\prime }-y x -x^{2}&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 45 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2}&=0 \end {array} \] |
✗ |
✓ |
✗ |
✗ |
|
| 46 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2}&=0 \end {array} \] |
✗ |
✓ |
✗ |
✗ |
|
| 47 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y^{\prime }}{x}-y x -x^{2}-\frac {1}{x}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 48 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 49 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 50 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{3} y^{\prime }-y x -x^{3}-x^{2}&=0 \end {array} \] |
✗ |
✗ |
✗ |
✗ |
|
| 51 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 52 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3}&=0 \end {array} \] |
✗ |
✗ |
✗ |
✗ |
|
| 50 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+c y^{\prime }+k y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime }&=-\frac {1}{2}-\frac {\sqrt {1-12 w}}{2}\\ w \left (1\right )&=-1\\ \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right )\\ y \left (0\right )&=1\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right )\\ y^{\prime }\left (0\right )&=1\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right )\\ y^{\prime }\left (0\right )&=1\\ y \left (0\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right )\\ y \left (1\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right )\\ y^{\prime }\left (1\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right )\\ y^{\prime }\left (1\right )&=0\\ y \left (0\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right )\\ y^{\prime }\left (1\right )&=0\\ y \left (2\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right )\\ y^{\prime }\left (1\right )&=0\\ y \left (0\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right )\\ y^{\prime }\left (1\right )&=0\\ y \left (2\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right )\\ y^{\prime }\left (1\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right )\\ y^{\prime }\left (1\right )&=0\\ y \left (2\right )&=0\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }+y&=x\\ y^{\prime }\left (0\right )&=0\\ y \left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1\\ \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 15 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 17 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 18 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 19 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=x \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 20 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+y x&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
|
| 21 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 22 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=x \end {array} \] |
✓ |
✓ |
✗ |
✗ |
|
| 23 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} x&=1 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2}&=0 \end {array} \] |
✗ |
✗ |
✗ |
✗ |
|
| 25 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 26 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 27 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 28 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{-\frac {y}{x}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 29 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 30 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+y&=8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 31 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} v v^{\prime }&=\frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=1 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x +1 \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2}+x +1 \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2}+1 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{4} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=1+\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x \sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=\cos \left (x \right )+\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+y \,{\mathrm e}^{x}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 15 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
|
| 16 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 17 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+2 y^{\prime }+y x&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 18 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y x&=x^{2}+2 x \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 19 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=1 \end {array} \]
Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✗ |
|
| 20 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=1 \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 21 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (-6+x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 22 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 23 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{2}+\cos \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=\cos \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{3}+\cos \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{3} \cos \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=x^{3} \cos \left (x \right )+\sin \left (x \right )^{2} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=\ln \left (x \right ) \end {array} \]
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
|
| 25 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 26 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 27 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 28 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+y^{2}&=\sec \left (x \right )^{4} \end {array} \] |
✗ |
✗ |
✗ |
✗ |
|
| 29 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y-2 x y^{\prime }\right )^{2}&={y^{\prime }}^{3} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 31 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 32 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }+x y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 33 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 34 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }+x y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 35 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 36 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x -1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 37 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ |
|
| 38 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 39 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -5\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 40 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 41 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=x \sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 42 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=\sin \left (x \right ) \cos \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 43 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=x^{3}+x \sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 44 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime \prime }+2 x y^{\prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 45 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 46 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 47 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 48 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 49 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 50 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-8\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 51 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 52 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 53 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 54 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }+\left (-x +2\right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 55 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 56 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 57 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 58 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ |
|
| 59 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 60 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y \left (1-y^{2}\right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 61 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {x y^{\prime \prime }}{1-x}+y&=\frac {1}{1-x} \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 62 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {x y^{\prime \prime }}{1-x}+y x&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 63 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {x y^{\prime \prime }}{1-x}+y&=\cos \left (x \right ) \end {array} \] |
✗ |
✓ |
✓ |
✗ |
|
| 64 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {x y^{\prime \prime }}{-x^{2}+1}+y&=0 \end {array} \] |
✗ |
✗ |
✗ |
✗ |
|
| 65 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left (x^{2}+3\right ) y \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 66 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (x -1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 67 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right )+2 t +1\\ y^{\prime }\left (t \right )&=5 x \left (t \right )+y \left (t \right )+3 t -1\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 68 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+20 y^{\prime }+500 y&=100000 \cos \left (100 x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 69 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=A y^{{2}/{3}} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=6 x^{3} {\mathrm e}^{x} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=\frac {1}{x^{2}} \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 15 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}}&=b^{2} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| 16 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-24 y&=16-\left (x +2\right ) {\mathrm e}^{4 x} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 17 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -2}\\ y \left (1\right )&=4\\ y^{\prime }\left (1\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 18 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&={\mathrm e}^{a \cos \left (x \right )} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 19 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{2 \ln \left (y\right ) y+y-x} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 20 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \end {array} \] | ✓ | ✓ | ✓ | ✗ |
|
| 21 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+{\mathrm e}^{-y}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 22 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+{\mathrm e}^{y}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
|
| 23 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y x +3 x -2 y+6}{y x -3 x -2 y+6} \end {array} \] |
✗ |
✗ |
✗ |
✗ |
|