|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-k^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+3 y^{\prime }-54 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-m^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 y^{\prime \prime }+5 y^{\prime }-12 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 9 y^{\prime \prime }+18 y^{\prime }-16 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+8 y^{\prime }+25 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-y = 2+5 x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{\frac {5 x}{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+4 y = x \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-a^{2} y = {\mathrm e}^{a x}+{\mathrm e}^{n x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+n^{2} y = {\mathrm e}^{x} x^{4}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y^{\prime }+y = \sin \left (2 x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-y = x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = {\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-9 y^{\prime }+20 y = 20 x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 2 \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+y = 3 x^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (1+x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (2 x -1\right )^{3} y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\]
|
✗ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = x^{2} \sin \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+a^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = \frac {a}{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime } \sin \left (x \right )^{2} = 2 y
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} a y^{\prime \prime } = y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-x^{2} y^{\prime }+x y = x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x} = n^{2} y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-2 b y^{\prime }+b^{2} x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = x \left (-x^{2}+1\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+x y^{\prime }-y = f \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{r} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-n^{2} y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x^{\prime \prime }+5 x^{\prime }-12 x = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+3 y^{\prime }-54 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 9 x^{\prime \prime }+18 x^{\prime }-16 x = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-y = 2+5 x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y = \sec \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-x}
\]
|
✓ |
✓ |
✓ |
|