|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} x^{2} y^{\prime \prime }+\left (a \,x^{3 n}+b \,x^{2 n}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+\left (a \,x^{2 n} \left (b \,x^{n}+c \right )^{m}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x \left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{3}+B \,x^{2}+C x +d \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a b \,x^{n}+a c \,x^{n -1}+b^{2} x^{2}+2 b x c +c^{2}-c \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n +2 m}-b^{2} x^{4 m +2}+a m \,x^{n -1}-m^{2}-m \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+\left (a \,x^{n +2}+b \,x^{2}+c \right ) y^{\prime }+\left (a n \,x^{n +1}+a c \,x^{n}+b c \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x -\left (a \,x^{n}-a b \,x^{n -1}+b \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (a \,x^{3}+x^{2}+b \right ) y^{\prime \prime }+a^{2} x \left (x^{2}-b \right ) y^{\prime }-a^{3} b x y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }-\left (-\lambda ^{2}+x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} 2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\lambda y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\left (\alpha \gamma +\beta \right ) x +\beta \lambda \right ) y^{\prime }-\left (\alpha x +\beta \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{4} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{4} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a \,x^{n -1}+a b \,x^{n -2}+b^{2}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-\left (b \,x^{n +1}+a \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (a -1\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{n} y^{\prime \prime }+\left (2 x^{n -1}+a \,x^{2}+b x \right ) y^{\prime }+b y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n}-x^{n -1}+a b x +b \right ) y^{\prime }+y a^{2} b x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{n} y^{\prime \prime }+\left (a \,x^{m +n}+1\right ) y^{\prime }+a \,x^{m} \left (1+m \,x^{n -1}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (c \,x^{n}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{n}+d -\lambda b \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (a \,x^{n}+b x +c \right ) y^{\prime \prime } = a n \left (n -1\right ) x^{n -2} y
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{n -2} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{n -2} \left (b \,x^{1+m}+a n -a \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+c \,x^{m} \left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{m}-a n \,x^{n -1}-1\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (a \,x^{n +1}+b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-a n -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-b n +\beta \right ) x^{n -2}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda -x \right ) y^{\prime }+y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} 2 \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+a n \,x^{n -1} b m \,x^{m -1} y^{\prime }+d y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{x \mu } \left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+\mu \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{x \mu }+\lambda \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 x \mu }+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 x \mu }\right )-\mu \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+{\mathrm e}^{\lambda x} a c +b \mu \,{\mathrm e}^{x \mu }\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +2 b \,{\mathrm e}^{x \mu }-\lambda \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+c \,{\mathrm e}^{2 \lambda x}+b^{2} {\mathrm e}^{2 x \mu }+b \left (\mu -\lambda \right ) {\mathrm e}^{x \mu }\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{x \left (\lambda +\mu \right )}+a \lambda \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{x \mu }-2 \lambda \right ) y^{\prime }+a^{2} b \lambda \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x} y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+a \,{\mathrm e}^{b \,x^{n}} y^{\prime }+c \left (a \,{\mathrm e}^{b \,x^{n}}-c \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }-a \,\lambda ^{2} {\mathrm e}^{\lambda x} y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (a^{2} {\mathrm e}^{2 \lambda x}+b \right ) y^{\prime \prime }-b \lambda y^{\prime }-a^{2} \lambda ^{2} k^{2} {\mathrm e}^{2 \lambda x} y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} 2 \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }+a \lambda \,{\mathrm e}^{\lambda x} y^{\prime }+c y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+k \left (\left (-a k +c \right ) {\mathrm e}^{\lambda x}+d -b k \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+\left (n \,{\mathrm e}^{\lambda x}+m \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} {\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x} = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (x -y^{\prime }-y\right )^{2} = x^{2} \left (2 x y-y^{\prime } x^{2}\right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-2 n x \left (1+x \right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{4} y^{\prime \prime }+2 x^{3} \left (1+x \right ) y^{\prime }+n^{2} y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{2} \left (-x^{3}+1\right ) y^{\prime \prime }-x^{3} y^{\prime }-2 y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2} = 0
\]
|
✗ |
✓ |
✓ |
|
|
\[
{} {x^{\prime }}^{2}+t x = \sqrt {t +1}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} f \left (t \right ) x^{\prime \prime }+x g \left (t \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+4 y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right )+\frac {x \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}, y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {y \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}\right ]
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{\prime \prime }+\left (1+x^{2}\right ) x^{\prime }+x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x = {y^{\prime }}^{3}-y^{\prime }+2
\]
|
✗ |
✓ |
✓ |
|
|
\[
{} y = {y^{\prime }}^{4}-{y^{\prime }}^{3}-2
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = x y^{3}+x^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y = x^{2}+2 x y^{\prime }+\frac {{y^{\prime }}^{2}}{2}
\]
|
✗ |
✓ |
✓ |
|
|
\[
{} {y^{\prime \prime }}^{3}+y^{\prime \prime }+1 = x
\]
|
✗ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \sin \left (x y\right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = \ln \left (x y\right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2} = \sin \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}+x y {y^{\prime }}^{2} = \ln \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} {y^{\prime \prime \prime }}^{2}+\sqrt {y} = \sin \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right ) = x^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime } x^{2}+y \sin \left (x \right ) = \sinh \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {k x}{y^{4}} = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}} = \frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} t^{2} y^{\prime \prime }-6 t y^{\prime }+y \sin \left (2 t \right ) = \ln \left (t \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+t y^{\prime }-\ln \left (t \right ) y = \cos \left (2 t \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x-x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x+x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
|
✗ |
✗ |
✓ |
|