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ODE |
Mathematica |
Maple |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y = {\mathrm e}^{2 x}
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime } = m^{2} y
\] |
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\[
{}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}
\] |
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\[
{}x y^{\prime \prime }+\left (x^{2}+1\right ) y^{\prime }+2 x y = 2 x
\] |
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\[
{}\left (x +2\right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = x \left (-x^{2}+1\right )^{{3}/{2}}
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
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\[
{}[t x^{\prime }\left (t \right )+y \left (t \right ) = 0, t y^{\prime }\left (t \right )+x \left (t \right ) = 0]
\] |
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\[
{}-x y^{\prime }+y = 0
\] |
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\[
{}\cot \left (y\right )-\tan \left (x \right ) y^{\prime } = 0
\] |
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\[
{}x^{3}+x y^{2}+a^{2} y+\left (y^{3}+x^{2} y-x \,a^{2}\right ) y^{\prime } = 0
\] |
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\[
{}\left (x +2 y^{3}\right ) y^{\prime } = y
\] |
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\[
{}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\] |
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\[
{}1+y^{2}-x y y^{\prime } = 0
\] |
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\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = \frac {6 x -2 y-7}{2 x +3 y-6}
\] |
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\[
{}2 x +y+1+\left (4 x +2 y-1\right ) y^{\prime } = 0
\] |
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\[
{}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 1
\] |
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\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
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\[
{}\left (x +2 y^{3}\right ) y^{\prime } = y
\] |
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\[
{}y^{\prime }+p \left (x \right ) y = q \left (x \right ) y^{n}
\] |
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\[
{}y^{\prime }+x \sin \left (2 y\right ) = x^{3} \cos \left (y\right )^{2}
\] |
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\[
{}a^{2}-2 x y-y^{2}-\left (x +y\right )^{2} y^{\prime } = 0
\] |
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\[
{}x^{2} y-\left (y^{3}+x^{3}\right ) y^{\prime } = 0
\] |
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\[
{}\left (x y \sin \left (x y\right )+\cos \left (x y\right )\right ) y+\left (x y \sin \left (x y\right )-\cos \left (x y\right )\right ) y^{\prime } = 0
\] |
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\[
{}y+\frac {y^{3}}{3}+\frac {x^{2}}{2}+\frac {\left (x y^{2}+x \right ) y^{\prime }}{4} = 0
\] |
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\[
{}3 x^{2} y^{4}+2 x y+\left (2 y^{2} x^{3}-x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
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\[
{}2 y^{\prime \prime }+9 y^{\prime }-18 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }+n^{2} y = \sec \left (n x \right )
\] |
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\[
{}y^{\prime \prime \prime }+y = \left (1+{\mathrm e}^{x}\right )^{2}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+y = a \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime \prime }+a^{2} y^{\prime } = \sin \left (a x \right )
\] |
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\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = {\mathrm e}^{x}+\cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \sinh \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right )
\] |
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\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
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\[
{}x^{2} \left ({y^{\prime }}^{2}-y^{2}\right )+y^{2} = x^{4}+2 x y y^{\prime }
\] |
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\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x = 0
\] |
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\[
{}{y^{\prime }}^{3} \left (x +2 y\right )+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (y+2 x \right ) y^{\prime } = 0
\] |
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\[
{}y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = b
\] |
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\[
{}y = \frac {x}{y^{\prime }}-a y^{\prime }
\] |
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\[
{}{y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\] |
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\[
{}{y^{\prime }}^{3} x = a +b y^{\prime }
\] |
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\[
{}y^{\prime } = \tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right )
\] |
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\[
{}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\] |
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\[
{}y = \left (1+y^{\prime }\right ) x +{y^{\prime }}^{2}
\] |
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\[
{}{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{y^{\prime }}^{3} {\mathrm e}^{2 y} = 0
\] |
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\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
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\[
{}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\] |
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\[
{}y-2 x y^{\prime }+a y {y^{\prime }}^{2} = 0
\] |
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\[
{}x^{2} \left (-x y^{\prime }+y\right ) = y {y^{\prime }}^{2}
\] |
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\[
{}x y \left (-x y^{\prime }+y\right ) = x +y y^{\prime }
\] |
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\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{\prime } y^{3}+x^{3}
\] |
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\[
{}3 y {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\] |
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\[
{}\left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\] |
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\[
{}\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\] |
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\[
{}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
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\[
{}{y^{\prime }}^{2} \left (-x^{2}+1\right ) = 1-y^{2}
\] |
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\[
{}y^{2} \left (1+{y^{\prime }}^{2}\right ) = r^{2}
\] |
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\[
{}\sin \left (x y^{\prime }\right ) \cos \left (y\right ) = \cos \left (x y^{\prime }\right ) \sin \left (y\right )+y^{\prime }
\] |
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\[
{}4 x {y^{\prime }}^{2} = \left (3 x -a \right )^{2}
\] |
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\[
{}4 {y^{\prime }}^{2} x \left (x -a \right ) \left (x -b \right ) = \left (3 x^{2}-2 x \left (a +b \right )+a b \right )^{2}
\] |
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\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
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\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
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\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3} = 0
\] |
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\[
{}x^{2} {y^{\prime }}^{3}+y y^{\prime } \left (y+2 x \right )+y^{2} = 0
\] |
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\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y = 0
\] |
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\[
{}{y^{\prime }}^{2} y^{2} \cos \left (a \right )^{2}-2 y^{\prime } x y \sin \left (a \right )^{2}+y^{2}-x^{2} \sin \left (a \right )^{2} = 0
\] |
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\[
{}\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x y+x^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\] |
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\[
{}x^{4} y^{\prime \prime \prime }+2 x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y = 1
\] |
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\[
{}x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{2}+3 x
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 2 x^{2}
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 x +\frac {10}{x}
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\] |
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\[
{}\left (2 x -1\right )^{3} y^{\prime \prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y = 0
\] |
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\[
{}\left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x
\] |
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\[
{}16 \left (1+x \right )^{4} y^{\prime \prime \prime \prime }+96 \left (1+x \right )^{3} y^{\prime \prime \prime }+104 \left (1+x \right )^{2} y^{\prime \prime }+8 \left (1+x \right ) y^{\prime }+y = x^{2}+4 x +3
\] |
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\[
{}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\] |
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\[
{}2 x^{2} y y^{\prime \prime }+4 y^{2} = x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\] |
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\[
{}\left (x^{2}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y^{\prime } = 0
\] |
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\[
{}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = \frac {2}{x^{3}}
\] |
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\[
{}y^{\prime \prime \prime }+\cos \left (x \right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
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\[
{}\sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\] |
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\[
{}2 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (7 x +3\right ) y^{\prime }-3 y = x^{2}
\] |
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\[
{}2 x^{2} \cos \left (y\right ) y^{\prime \prime }-2 x^{2} \sin \left (y\right ) {y^{\prime }}^{2}+x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = \ln \left (x \right )
\] |
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\[
{}x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2} = 0
\] |
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\[
{}y+3 x y^{\prime }+2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{\prime } y^{2}\right ) y^{\prime \prime } = 0
\] |
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