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ODE |
Mathematica |
Maple |
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\[
{}y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 x \mu }+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 x \mu }\right )-\mu \right ) y = 0
\] |
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\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
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\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
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\[
{}{\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x} = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 n x \left (1+x \right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+2 x^{3} \left (1+x \right ) y^{\prime }+n^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2} = 0
\] |
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\[
{}\sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x = 0
\] |
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\[
{}x = {y^{\prime }}^{3}-y^{\prime }+2
\] |
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\[
{}y = {y^{\prime }}^{4}-{y^{\prime }}^{3}-2
\] |
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\[
{}y = x^{2}+2 x y^{\prime }+\frac {{y^{\prime }}^{2}}{2}
\] |
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\[
{}{y^{\prime \prime }}^{3}+y^{\prime \prime }+1 = x
\] |
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\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {k x}{y^{4}} = 0
\] |
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\[
{}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+{y^{\prime }}^{3} = 0
\] |
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\[
{}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right )
\] |
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\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
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\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
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\[
{}S^{\prime } = S^{3}-2 S^{2}+S
\] |
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\[
{}y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\] |
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\[
{}y^{\prime } = \cos \left (y\right )
\] |
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\[
{}w^{\prime } = w \cos \left (w\right )
\] |
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\[
{}w^{\prime } = w \cos \left (w\right )
\] |
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\[
{}w^{\prime } = w \cos \left (w\right )
\] |
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\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
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\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
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\[
{}y y^{\prime }+y^{4} = \sin \left (x \right )
\] |
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\[
{}1 = \cos \left (y\right ) y^{\prime }
\] |
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\[
{}y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = \sqrt {x -y}
\] |
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\[
{}{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0
\] |
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\[
{}{y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0
\] |
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\[
{}y \ln \left (y\right )+x y^{\prime } = 1
\] |
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\[
{}x^{2} y^{\prime } \cos \left (y\right )+1 = 0
\] |
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\[
{}x^{2} y^{\prime }+\cos \left (2 y\right ) = 1
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0
\] |
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\[
{}x^{2} y^{\prime }+\sin \left (2 y\right ) = 1
\] |
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\[
{}\frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\] |
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\[
{}3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0
\] |
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\[
{}\frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
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\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
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\[
{}8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x
\] |
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\[
{}y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right )
\] |
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\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
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\[
{}3 y^{\prime } y^{\prime \prime } = 2 y
\] |
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\[
{}y^{\prime \prime \prime } = 3 y y^{\prime }
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right )
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right )
\] |
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\[
{}2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}
\] |
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\[
{}y^{\prime \prime }+\alpha ^{2} y = 1
\] |
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\[
{}\ln \left (x \right ) y^{\prime \prime }-y \sin \left (x \right ) = 0
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = \frac {t +y \left (t \right )}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )}\right ]
\] |
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\[
{}[x^{\prime \prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ) x^{\prime }\left (t \right )+x \left (t \right )]
\] |
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\[
{}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+4, y^{\prime }\left (t \right ) = -2 x \left (t \right )+\sin \left (t \right ) y \left (t \right )]
\] |
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\[
{}y = 2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2}
\] |
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\[
{}y = \frac {k \left (y y^{\prime }+x \right )}{\sqrt {1+{y^{\prime }}^{2}}}
\] |
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\[
{}y = 2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2}
\] |
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\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime } = y^{\prime } {\mathrm e}^{y}
\] |
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\[
{}y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x}
\] |
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\[
{}2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
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\[
{}y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 x y y^{\prime }+3 x^{2} y^{2}\right ) y^{\prime }+x^{3} y^{3} = 0
\] |
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\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
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\[
{}{y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\] |
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\[
{}{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\] |
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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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\[
{}y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = m^{2}
\] |
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\[
{}x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\] |
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\[
{}{y^{\prime }}^{2}-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}
\] |
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\[
{}{x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right )
\] |
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\[
{}x^{2} {y^{\prime }}^{3}+y \left (1+x^{2} y\right ) {y^{\prime }}^{2}+y^{\prime } y^{2} = 0
\] |
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\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
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\[
{}y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\] |
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\[
{}y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\] |
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\[
{}x y^{\prime \prime } \left (x \cos \left (x \right )-2 \sin \left (x \right )\right )+\left (x^{2}+2\right ) y^{\prime } \sin \left (x \right )-2 \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y = 0
\] |
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\[
{}{y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\] |
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\[
{}y^{\prime } = \tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right )
\] |
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\[
{}{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\] |
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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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\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
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\[
{}x^{2} {y^{\prime }}^{3}+y y^{\prime } \left (y+2 x \right )+y^{2} = 0
\] |
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