|
# |
ODE |
Mathematica |
Maple |
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y = \cos \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 x y y^{\prime }+6 y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} \left (-x^{3}+1\right ) y^{\prime \prime }-x^{3} y^{\prime }-2 y = 0
\] |
✗ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2} = 0
\] |
✗ |
✓ |
|
|
\[
{}x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }-\left (x y^{\prime }-y\right )^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )-x^{2} y^{2}
\] |
✓ |
✓ |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2+4 x \right ) y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|
|
\[
{}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0
\] |
✓ |
✓ |
|
|
\[
{}x \left (x +2 y\right ) y^{\prime \prime }+2 x {y^{\prime }}^{2}+4 \left (x +y\right ) y^{\prime }+2 y+x^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}[3 x^{\prime }\left (t \right )+3 x \left (t \right )+2 y \left (t \right ) = {\mathrm e}^{t}, 4 x \left (t \right )-3 y^{\prime }\left (t \right )+3 y \left (t \right ) = 3 t]
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{t}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = -\frac {t}{x}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{-x}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }+2 x = t^{2}+4 t +7
\] |
✓ |
✓ |
|
|
\[
{}2 t x^{\prime } = x
\] |
✓ |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }-6 x = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x^{\prime \prime }-5 x^{\prime }-3 x = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = x \left (1-\frac {x}{4}\right )
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = x^{2}+t^{2}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = t \cos \left (t^{2}\right )
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {t +1}{\sqrt {t}}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime \prime } = -3 \sqrt {t}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = t \,{\mathrm e}^{-2 t}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {1}{t \ln \left (t \right )}
\] |
✓ |
✓ |
|
|
\[
{}\sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right )
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }+t x^{\prime \prime } = 1
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \sqrt {x}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{-2 x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
✓ |
✓ |
|
|
\[
{}u^{\prime } = \frac {1}{5-2 u}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = a x+b
\] |
✓ |
✓ |
|
|
\[
{}Q^{\prime } = \frac {Q}{4+Q^{2}}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = r \left (a -y\right )
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{t +1}
\] |
✓ |
✓ |
|
|
\[
{}\theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right )
\] |
✓ |
✓ |
|
|
\[
{}\left (2 u+1\right ) u^{\prime }-t -1 = 0
\] |
✓ |
✓ |
|
|
\[
{}R^{\prime } = \left (t +1\right ) \left (1+R^{2}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y+\frac {1}{y} = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (t +1\right ) x^{\prime }+x^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{2 y+1}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \left (4 t -x\right )^{2}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = 2 t x^{2}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = t^{2} {\mathrm e}^{-x}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = x \left (4+x\right )
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{t +x}
\] |
✓ |
✓ |
|
|
\[
{}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = t^{2} \tan \left (y\right )
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {\left (4+2 t \right ) x}{\ln \left (x\right )}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {t^{2}}{1-x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = 6 t \left (x-1\right )^{{2}/{3}}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 t x}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t} = {\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}\frac {x^{\prime }+t x^{\prime \prime }}{t} = -2
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = 2 t^{3} x-6
\] |
✓ |
✓ |
|
|
\[
{}\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = t -x^{2}
\] |
✓ |
✓ |
|
|
\[
{}7 t^{2} x^{\prime } = 3 x-2 t
\] |
✓ |
✓ |
|
|
\[
{}x x^{\prime } = 1-t x
\] |
✓ |
✓ |
|
|
\[
{}{x^{\prime }}^{2}+t x = \sqrt {t +1}
\] |
✗ |
✗ |
|
|
\[
{}x^{\prime } = -\frac {2 x}{t}+t
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }+2 t x = {\mathrm e}^{-t^{2}}
\] |
✓ |
✓ |
|
|
\[
{}t x^{\prime } = -x+t^{2}
\] |
✓ |
✓ |
|
|
\[
{}\theta ^{\prime } = -a \theta +{\mathrm e}^{b t}
\] |
✓ |
✓ |
|
|
\[
{}\left (t^{2}+1\right ) x^{\prime } = -3 t x+6 t
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }+\frac {5 x}{t} = t +1
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \left (a +\frac {b}{t}\right ) x
\] |
✓ |
✓ |
|
|
\[
{}R^{\prime }+\frac {R}{t} = \frac {2}{t^{2}+1}
\] |
✓ |
✓ |
|
|
\[
{}N^{\prime } = N-9 \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}\cos \left (\theta \right ) v^{\prime }+v = 3
\] |
✓ |
✓ |
|
|
\[
{}R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+a y = \sqrt {t +1}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = 2 t x
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }+\frac {{\mathrm e}^{-t} x}{t} = t
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 3 t
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \left (t +x\right )^{2}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = a x+b
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }+p \left (t \right ) x = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x}
\] |
✓ |
✓ |
|