|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \frac {x +y y^{\prime }}{x y^{\prime }-y} = \sqrt {\frac {a^{2}-x^{2}-y^{2}}{x^{2}+y^{2}}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }-y = x \sqrt {x^{2}+y^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x \left (x^{2}+y^{2}-a^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x +y y^{\prime } = m \left (x y^{\prime }-y\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y \left (2 x^{2} y+{\mathrm e}^{x}\right )-\left ({\mathrm e}^{x}+y^{3}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right )
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x^{2}+y^{2}+x -\left (2 x^{2}+2 y^{2}-y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y \left (1+\frac {1}{x}\right )+\cos \left (y\right )+\left (x +\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2}-a y = \left (a x -y^{2}\right ) y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y-x y^{\prime }+x^{2}+1+x^{2} \sin \left (y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \sec \left (y\right )^{2} y^{\prime }+2 x \tan \left (y\right ) = x^{3}
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} {y^{\prime }}^{3}+y \left (1+x^{2} y\right ) {y^{\prime }}^{2}+y^{2} y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}-y y^{\prime }+x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y = x {y^{\prime }}^{2}+y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y = \sin \left (y^{\prime }\right )-y^{\prime } \cos \left (y^{\prime }\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y = y^{\prime } \tan \left (y^{\prime }\right )+\ln \left (\cos \left (y^{\prime }\right )\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x = y y^{\prime }-{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x -b \right ) y^{\prime } = y-a y {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y {y^{\prime }}^{2}+2 x y^{\prime } = y
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y = x y^{\prime }+\frac {a}{y^{\prime }}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y = x y^{\prime }+y^{\prime }-{y^{\prime }}^{3}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y = x y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y = x y^{\prime }+\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (y-x y^{\prime }\right ) \left (y^{\prime }-1\right ) = y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x {y^{\prime }}^{2}-y y^{\prime }+a = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y = x y^{\prime }+{y^{\prime }}^{3}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} \left (x y^{\prime }-y\right )^{2} = a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}}
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} 2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (x \cos \left (x \right )-4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+\sin \left (2 x \right ) x = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x y^{\prime }-y\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} \left (y-x y^{\prime }\right ) = y {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }+y^{2}+a^{4} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x +y y^{\prime } = a {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 y = x y^{\prime }+\frac {a}{y^{\prime }}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a {y^{\prime }}^{2}-b \right ) x y+\left (b \,x^{2}-y^{2} a +c \right ) y^{\prime } = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} \left (1+6 y^{2}-3 x^{2} y\right ) y^{\prime } = 3 x y^{2}-x^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = 1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = \left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x y^{\prime }-y\right ) \left (x +y y^{\prime }\right ) = h^{2} y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{2}-3 x y y^{\prime } = 2 y^{2}+x^{3}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = m
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (8 {y^{\prime }}^{3}-27\right ) x = \frac {12 {y^{\prime }}^{2}}{x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 y = 2 x y^{\prime }-\frac {2 {y^{\prime }}^{2}}{x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{2} \left (y-x y^{\prime }\right ) = x^{4} {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{4} = 4 y \left (x y^{\prime }-2 y\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y+x^{2} = {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{3} = y^{4} \left (x y^{\prime }+y\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1-y^{\prime }\right )^{2}-{\mathrm e}^{-2 y} = {y^{\prime }}^{2} {\mathrm e}^{-2 x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a x y {y^{\prime }}^{2}+\left (x^{2}-y^{2} a -b \right ) y^{\prime }-x y = 0
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} {y^{\prime }}^{2} = \left (4 y+1\right ) \left (y^{\prime }-y\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+b^{2}-y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}-1\right ) y^{\prime }+x y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-x y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 8 {y^{\prime }}^{3} x = y \left (12 {y^{\prime }}^{2}-9\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2} y^{\prime }+y^{2}\right ) \left (x y^{\prime }+y\right ) = \left (1+y^{\prime }\right )^{2}
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} \left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right ) = 2 y^{\prime }
\]
|
✓ |
✗ |
✗ |
|
|
\[
{} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+{\mathrm e}^{x} \left (y^{\prime }+y\right ) = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}-x \right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-4 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 2 x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (6 x +3\right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y y^{\prime \prime }+x {y^{\prime }}^{2}+y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime \prime }+4 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+3 x y = 2
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y = \ln \left (x \right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y = 2 x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{2}+\left (2 x y-1\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {a^{2}}{y} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = y^{3}-y
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = {\mathrm e}^{2 y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} {y^{\prime }}^{2}+y y^{\prime \prime } = 1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime \prime } y^{\prime \prime } = 2
\]
|
✓ |
✓ |
✗ |
|