| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = -m^{2} y
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime }+x y^{\prime \prime } = x y
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-{y^{\prime }}^{2}-{y^{\prime }}^{3} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = r y^{\prime \prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime } = y^{2} \left (1+y^{2}\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }+2 y = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y = \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e y^{\prime \prime } = -P \left (L -x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} e y^{\prime \prime } = P \left (a -y\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y^{\prime }+x y^{\prime \prime } = 2 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y+4 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\csc \left (x \right )^{2} y = \cos \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime } = \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = -a^{2} y
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = \frac {1}{y^{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 1
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime \prime }+3 y^{\prime } = 3 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x = y^{\prime \prime }+y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
| \[
{} V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} V^{\prime \prime }+\frac {V^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-k^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime }-54 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-m^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y^{\prime \prime }+5 y^{\prime }-12 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 9 y^{\prime \prime }+18 y^{\prime }-16 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+8 y^{\prime }+25 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = 5 x +2
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{\frac {5 x}{2}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+\cos \left (2 x \right ) {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = x \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -a^{2} y+y^{\prime \prime } = {\mathrm e}^{a x}+{\mathrm e}^{n x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+n^{2} y = x^{4} {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }+y^{\prime }+y = \sin \left (2 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-y = x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime }-4 y^{\prime }+3 y = \cos \left (2 x \right ) {\mathrm e}^{x}+\cos \left (3 x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 20 y-9 y^{\prime }+y^{\prime \prime } = 20 x
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 2 \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+y = 3 x^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (1+x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (2 x +5\right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (2 x -1\right )^{3} y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime } = x y^{2}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = x^{2} \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|