|
# |
ODE |
Mathematica |
Maple |
|
\[
{}\left (\operatorname {g0} \left (x \right )+y \operatorname {g1} \left (x \right )\right ) y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3}
\] |
✗ |
✗ |
|
|
\[
{}\left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime } = y^{3} \csc \left (x \right ) \sec \left (x \right )
\] |
✓ |
✗ |
|
|
\[
{}\left (x \,a^{2}+y \left (x^{2}-y^{2}\right )\right ) y^{\prime }+x \left (x^{2}-y^{2}\right ) = a^{2} y
\] |
✓ |
✗ |
|
|
\[
{}{y^{\prime }}^{2}+a \,x^{2}+b y = 0
\] |
✓ |
✗ |
|
|
\[
{}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right )
\] |
✗ |
✗ |
|
|
\[
{}{y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x \left (x^{2}+x y-2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y = 0
\] |
✗ |
✗ |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
✓ |
✗ |
|
|
\[
{}y {y^{\prime }}^{2} x +\left (a +x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
✓ |
✗ |
|
|
\[
{}y {y^{\prime }}^{2} x -\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y = 0
\] |
✓ |
✗ |
|
|
\[
{}\left (a^{2}-2 a x y+y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\] |
✗ |
✗ |
|
|
\[
{}x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2} x^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0
\] |
✗ |
✗ |
|
|
\[
{}x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } \ln \left (y^{\prime }+\sqrt {a +{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}\frac {x^{n} y^{\prime }}{b y^{2}-c \,x^{2 a}}-\frac {a y x^{a -1}}{b y^{2}-c \,x^{2 a}}+x^{a -1} = 0
\] |
✗ |
✗ |
|
|
\[
{}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }-\left (2 x -1\right ) y = 0
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}} = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+y = x^{{3}/{2}}
\] |
✓ |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = \sqrt {x}
\] |
✓ |
✗ |
|
|
\[
{}s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2}
\] |
✓ |
✗ |
|
|
\[
{}s^{2}+s^{\prime } = \frac {s+1}{s t}
\] |
✗ |
✗ |
|
|
\[
{}x^{\prime }+t x = {\mathrm e}^{x}
\] |
✗ |
✗ |
|
|
\[
{}x x^{\prime }+t^{2} x = \sin \left (t \right )
\] |
✗ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime }-x y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}}
\] |
✓ |
✗ |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+y = \cos \left (x \right )
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \cos \left (x \right )
\] |
✓ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (1+x \right ) y = 0
\] |
✓ |
✗ |
|
|
\[
{}x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y = 0
\] |
✗ |
✗ |
|
|
\[
{}t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0
\] |
✓ |
✗ |
|
|
\[
{}u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right )
\] |
✗ |
✗ |
|
|
\[
{}x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x = 0
\] |
✗ |
✗ |
|
|
\[
{}\sin \left (x^{\prime }\right )+y^{3} x = \sin \left (y \right )
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = 6 \sqrt {y}+5 x^{3}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
✗ |
✗ |
|
|
\[
{}m^{\prime } = -\frac {k}{m^{2}}
\] |
✓ |
✗ |
|
|
\[
{}x y^{\prime }-4 y = x^{6} {\mathrm e}^{x}
\] |
✗ |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{4} y^{\prime \prime }+\lambda y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y = 0
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
✗ |
✗ |
|
|
\[
{}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y = \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2}
\] |
✓ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y = 0
\] |
✓ |
✗ |
|
|
\[
{}[y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+x y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{2} \left (x \right )+x^{3} y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 x y_{1} \left (x \right )-y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right )]
\] |
✗ |
✗ |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3}
\] |
✗ |
✗ |
|
|
\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
✓ |
✗ |
|
|
\[
{}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\] |
✗ |
✗ |
|
|
\[
{}x y y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{3}
\] |
✓ |
✗ |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
✓ |
✗ |
|
|
\[
{}x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{4} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .
\] |
✓ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )+1, y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )]
\] |
✗ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = t y \left (t \right )+1, y^{\prime }\left (t \right ) = -t x \left (t \right )+y \left (t \right )]
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime \prime }+5 x y^{\prime }+\sqrt {x}\, y = 0
\] |
✗ |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
✓ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )+{\mathrm e}^{-t}-3 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{-t}+t, z^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right )+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t]
\] |
✓ |
✗ |
|
|
\[
{}y = x y^{\prime }+x^{3} {y^{\prime }}^{2}
\] |
✓ |
✗ |
|
|
\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
✗ |
✗ |
|
|
\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = \sqrt {-y^{2}-x^{2}+1}
\] |
✗ |
✗ |
|
|
\[
{}y y^{\prime \prime } = x
\] |
✗ |
✗ |
|
|
\[
{}3 y y^{\prime \prime } = \sin \left (x \right )
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0
\] |
✗ |
✗ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2} = 0
\] |
✗ |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1+x
\] |
✓ |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x
\] |
✓ |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+x +1
\] |
✓ |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )
\] |
✓ |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )+1
\] |
✓ |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \cos \left (x \right )+\sin \left (x \right )
\] |
✓ |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = 1
\] |
✓ |
✗ |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = \sec \left (x \right )^{4}
\] |
✗ |
✗ |
|
|
\[
{}\frac {x y^{\prime \prime }}{-x^{2}+1}+y = 0
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime }+y = \frac {1}{x}
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime }+y = \frac {1}{x^{2}}
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime \prime } = \frac {1}{x}
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{x}
\] |
✓ |
✗ |
|