|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y = \tan \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+4 y = x^{2}+\cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}+x^{3}-x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}-\cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-2 y^{\prime } = 1+{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }+6 y = x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 x^{3}-x \,{\mathrm e}^{3 x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+4 y = \sec \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y = x \cos \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-y^{\prime } x^{2}+x y = x
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 y \sin \left (x \right ) = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }+2 y^{\prime }-x y = 2 \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+y \,{\mathrm e}^{2 x} = {\mathrm e}^{4 x}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+x y^{\prime } = x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime } = {\mathrm e}^{x} x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (y^{\prime }-x y^{\prime \prime }\right )^{2} = 1+{y^{\prime \prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y = \cos \left (x \right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x \left (2 y+x \right ) y^{\prime \prime }+2 {y^{\prime }}^{2} x +4 \left (x +y\right ) y^{\prime }+2 y+x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{\prime \prime } = -3 \sqrt {t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime }+t x^{\prime \prime } = 1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \frac {x^{\prime }+t x^{\prime \prime }}{t} = -2
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime } = 3 t
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = 12
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = \left (t +2\right ) \sin \left (\pi t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+{\mathrm e}^{t} t
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x = t^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-4 x = \cos \left (2 t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-2 x^{\prime } = 4
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+3025 x = \cos \left (45 t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x = \tan \left (t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-x = {\mathrm e}^{t} t
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-x = \frac {1}{t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t^{2} x^{\prime \prime }-2 x = t^{3}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x = \frac {1}{t +1}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+\frac {x^{\prime }}{t} = a
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+9 x = \sin \left (3 t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-2 x = 1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (1-t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }-x = \delta \left (t -5\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x = \delta \left (t -2\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime \prime }+4 x = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 2-12 x +6 \,{\mathrm e}^{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-3 y^{\prime }+8 y = 4 x^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }+2 y^{\prime }+4 y = \cos \left (4 x \right )
\]
|
✓ |
✓ |
✓ |
|