| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime } = -\frac {a \left (n -1\right ) \sin \left (2 a x \right ) y^{\prime }}{\cos \left (a x \right )^{2}}-\frac {n \,a^{2} \left (\left (n -1\right ) \sin \left (a x \right )^{2}+\cos \left (a x \right )^{2}\right ) y}{\cos \left (a x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = \frac {2 y}{\sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {a y}{\sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }-\left (a \sin \left (x \right )^{2}+\left (n -1\right ) n \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {\left (-a^{2} \cos \left (x \right )^{2}-\left (3-2 a \right ) \cos \left (x \right )-3+3 a \right ) y}{\sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right )^{2} y^{\prime \prime }-\left (a^{2} \cos \left (x \right )^{2}+b \cos \left (x \right )+\frac {b^{2}}{\left (2 a -3\right )^{2}}+3 a +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {\left (-\left (a^{2} b^{2}-\left (a +1\right )^{2}\right ) \sin \left (x \right )^{2}-a \left (a +1\right ) b \sin \left (2 x \right )-\left (a -1\right ) a \right ) y}{\sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {\left (a \cos \left (x \right )^{2}+b \sin \left (x \right )^{2}+c \right ) y}{\sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}+\frac {y}{\sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (v \left (v +1\right ) \sin \left (x \right )^{2}-n^{2}\right ) y}{\sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = \frac {\cos \left (2 x \right ) y^{\prime }}{\sin \left (2 x \right )}-2 y
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {4 \sin \left (3 x \right ) y}{\sin \left (x \right )^{3}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {\left (4 v \left (v +1\right ) \sin \left (x \right )^{2}-\cos \left (x \right )^{2}+2-4 n^{2}\right ) y}{4 \sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = \frac {\left (3 \sin \left (x \right )^{2}+1\right ) y^{\prime }}{\cos \left (x \right ) \sin \left (x \right )}+\frac {\sin \left (x \right )^{2} y}{\cos \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {\left (-a \cos \left (x \right )^{2} \sin \left (x \right )^{2}-m \left (m -1\right ) \sin \left (x \right )^{2}-n \left (n -1\right ) \cos \left (x \right )^{2}\right ) y}{\cos \left (x \right )^{2} \sin \left (x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {\left (2 f \left (x \right ) {g^{\prime }\left (x \right )}^{2} g \left (x \right )-\left (g \left (x \right )^{2}-1\right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )\right ) y^{\prime }}{f \left (x \right ) g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}-\frac {\left (\left (g \left (x \right )^{2}-1\right ) \left (f^{\prime }\left (x \right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )-f \left (x \right ) f^{\prime \prime }\left (x \right ) g^{\prime }\left (x \right )\right )-\left (2 f^{\prime }\left (x \right ) g \left (x \right )+v \left (v +1\right ) f \left (x \right ) g^{\prime }\left (x \right )\right ) f \left (x \right ) {g^{\prime }\left (x \right )}^{2}\right ) y}{f \left (x \right )^{2} g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (x -1\right ) y}{x^{4}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (-x -1\right ) y}{x^{4}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -\frac {b^{2} y}{\left (-a^{2}+x^{2}\right )^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-6 y^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-6 y^{2}+4 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a y^{3} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+a \,x^{r} y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+6 a^{10} y^{11}-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-{\mathrm e}^{y} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a \sin \left (y\right )+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} -y^{3}+y y^{\prime }+y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+y y^{\prime }-y^{3}+a y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (3 a +y\right ) y^{\prime }-y^{3}+a y^{2}+2 a^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+f \left (x \right ) y^{2}+y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 a y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y y^{\prime }+b y^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} c y+b y^{\prime }+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} b y+a y {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a \left (x y^{\prime }-y\right )^{v} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = a \sqrt {b y^{2}+{y^{\prime }}^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 9 {y^{\prime }}^{4}+8 y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} b \,{\mathrm e}^{y} x +a y^{\prime }+x y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (y-1\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+{y^{\prime }}^{3}+2 x y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime } = a \left (y^{n}-y\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-\sqrt {b y^{2}+a \,x^{2} {y^{\prime }}^{2}} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} 2 y+a y^{3}+9 x^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime }-a \left (x y^{\prime }-y\right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime }+a^{2} y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime }-x^{2} y^{\prime } \left (x +y^{\prime }\right )+4 y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x y^{\prime }-y\right )^{3}+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sqrt {x}\, y^{\prime \prime }-y^{{3}/{2}} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x^{2} a +b x +c \right )^{{3}/{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {x^{2} a +b x +c}}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-\ln \left (y\right ) y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-f^{\prime }\left (x \right ) y-y^{3} = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-y f^{\prime \prime }\left (x \right )+f \left (x \right ) y^{3}-y^{4} = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }+b y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }-2 a y^{2}+b y^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-\left (-1+a y\right ) y^{\prime }+2 a^{2} y^{2}-2 y^{3} b^{2}+a y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (1+y\right ) \left (b^{2} y^{2}-a^{2}\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (g \left (x \right )+f \left (x \right ) y^{2}\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right ) = 0
\]
|
✓ |
✗ |
✗ |
|