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