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ODE |
Mathematica |
Maple |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+y = {\mathrm e}^{-x}+\cos \left (x \right )+x^{3}+{\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+y = {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )
\] |
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\[
{}y^{\left (6\right )}-2 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }+y = \sin \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = 16 x^{2}+256
\] |
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\[
{}y^{\prime \prime }+y = 3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3}
\] |
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\[
{}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = 96 \sin \left (2 x \right ) \cos \left (x \right )
\] |
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\[
{}y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 24 x \cos \left (x \right )
\] |
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\[
{}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\] |
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\[
{}{y^{\prime }}^{2}-5 y^{\prime }+6 = 0
\] |
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\[
{}{y^{\prime }}^{2}-9 y^{\prime }+18 = 0
\] |
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\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-3 x^{2} = 0
\] |
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\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
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\[
{}{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1 = 0
\] |
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\[
{}y^{\prime } \left (y^{\prime }-y\right ) = x \left (x +y\right )
\] |
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\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
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\[
{}x +y {y^{\prime }}^{2} = y^{\prime } \left (x y+1\right )
\] |
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\[
{}x {y^{\prime }}^{2}+\left (y-x \right ) y^{\prime }-y = 0
\] |
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\[
{}{y^{\prime }}^{3}-a \,x^{4} = 0
\] |
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\[
{}{y^{\prime }}^{2}+x y^{\prime }+y y^{\prime }+x y = 0
\] |
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\[
{}{y^{\prime }}^{3}-y^{\prime } \left (y^{2}+x y+x^{2}\right )+x y \left (x +y\right ) = 0
\] |
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\[
{}\left (y^{\prime }+y+x \right ) \left (y+x +x y^{\prime }\right ) \left (y^{\prime }+2 x \right ) = 0
\] |
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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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\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
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\[
{}{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 y^{2} y^{\prime } x = 0
\] |
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\[
{}{y^{\prime }}^{2} \left (2-3 y\right )^{2} = 4-4 y
\] |
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\[
{}y = 3 x +a \ln \left (y^{\prime }\right )
\] |
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\[
{}{y^{\prime }}^{2}-y y^{\prime }+x = 0
\] |
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\[
{}y = x +a \arctan \left (y^{\prime }\right )
\] |
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\[
{}3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0
\] |
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\[
{}y = x {y^{\prime }}^{2}+y^{\prime }
\] |
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\[
{}x {y^{\prime }}^{2}+a x = 2 y y^{\prime }
\] |
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\[
{}{y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y}
\] |
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\[
{}y = \sin \left (y^{\prime }\right )-y^{\prime } \cos \left (y^{\prime }\right )
\] |
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\[
{}y = \sin \left (x \right ) y^{\prime }+\cos \left (x \right )
\] |
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\[
{}y = y^{\prime } \tan \left (y^{\prime }\right )+\ln \left (\cos \left (y^{\prime }\right )\right )
\] |
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\[
{}x = y y^{\prime }-{y^{\prime }}^{2}
\] |
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\[
{}\left (2 x -b \right ) y^{\prime } = y-a y {y^{\prime }}^{2}
\] |
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\[
{}x = y+a \ln \left (y^{\prime }\right )
\] |
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\[
{}y {y^{\prime }}^{2}+2 x y^{\prime } = y
\] |
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\[
{}x \left (1+{y^{\prime }}^{2}\right ) = 1
\] |
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\[
{}x^{2} = a^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
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\[
{}y = x y^{\prime }+\frac {a}{y^{\prime }}
\] |
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\[
{}y = x y^{\prime }+y^{\prime }-{y^{\prime }}^{3}
\] |
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\[
{}y = x y^{\prime }+a y^{\prime } \left (1-y^{\prime }\right )
\] |
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\[
{}y = x y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}y = x y^{\prime }+\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}}
\] |
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\[
{}\left (-x y^{\prime }+y\right ) \left (y^{\prime }-1\right ) = y^{\prime }
\] |
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\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a = 0
\] |
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\[
{}y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\] |
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\[
{}y = x y^{\prime }+{y^{\prime }}^{3}
\] |
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\[
{}4 y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
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\[
{}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
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\[
{}x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} = a
\] |
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\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2} = x^{2}
\] |
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\[
{}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
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\[
{}y = \frac {2 a {y^{\prime }}^{2}}{\left (1+{y^{\prime }}^{2}\right )^{2}}
\] |
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\[
{}\left (x y^{\prime }-y\right )^{2} = a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}}
\] |
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\[
{}4 x {y^{\prime }}^{2}+4 y y^{\prime } = y^{4}
\] |
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\[
{}2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (x \cos \left (x \right )-4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+\sin \left (2 x \right ) x = 0
\] |
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\[
{}\left (x y^{\prime }-y\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\] |
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\[
{}-x y^{\prime }+y = x +y y^{\prime }
\] |
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\[
{}a^{2} y {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
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\[
{}x^{2} \left (-x y^{\prime }+y\right ) = y {y^{\prime }}^{2}
\] |
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\[
{}\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right ) = 0
\] |
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\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }+y^{2}+a^{4} = 0
\] |
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\[
{}x +y y^{\prime } = a {y^{\prime }}^{2}
\] |
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\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
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\[
{}2 y = x y^{\prime }+\frac {a}{y^{\prime }}
\] |
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\[
{}y = a y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}\left (a {y^{\prime }}^{2}-b \right ) x y+\left (b \,x^{2}-y^{2} a +c \right ) y^{\prime } = 0
\] |
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\[
{}y = a y^{\prime }+b {y^{\prime }}^{2}
\] |
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\[
{}{y^{\prime }}^{3}-\left (y+2 x -{\mathrm e}^{x -y}\right ) {y^{\prime }}^{2}+\left (2 x y-2 x \,{\mathrm e}^{x -y}-y \,{\mathrm e}^{x -y}\right ) y^{\prime }+2 x y \,{\mathrm e}^{x -y} = 0
\] |
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\[
{}\left (1+6 y^{2}-3 x^{2} y\right ) y^{\prime } = 3 x y^{2}-x^{2}
\] |
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\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = 1
\] |
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\[
{}\left (x^{3} y^{3}+x^{2} y^{2}+x y+1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-x y+1\right ) x y^{\prime } = 0
\] |
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\[
{}\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = \left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }
\] |
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\[
{}\left (x y^{\prime }-y\right ) \left (x +y y^{\prime }\right ) = h^{2} y^{\prime }
\] |
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\[
{}x^{2} y^{2}-3 x y y^{\prime } = 2 y^{2}+x^{3}
\] |
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\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
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\[
{}y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = m
\] |
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\[
{}y = x y^{\prime }-{y^{\prime }}^{2}
\] |
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\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
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\[
{}4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0
\] |
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\[
{}\left (8 {y^{\prime }}^{3}-27\right ) x = \frac {12 {y^{\prime }}^{2}}{x}
\] |
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\[
{}3 y = 2 x y^{\prime }-\frac {2 {y^{\prime }}^{2}}{x}
\] |
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\[
{}y^{2}+{y^{\prime }}^{2} = 1
\] |
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\[
{}{y^{\prime }}^{2} \left (2-3 y\right )^{2} = 4-4 y
\] |
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\[
{}4 x {y^{\prime }}^{2} = \left (3 x -1\right )^{2}
\] |
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\[
{}x {y^{\prime }}^{2}-\left (x -a \right )^{2} = 0
\] |
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\[
{}y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
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\[
{}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0
\] |
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\[
{}{y^{\prime }}^{2}+2 x^{3} y^{\prime }-4 x^{2} y = 0
\] |
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\[
{}y^{2} \left (-x y^{\prime }+y\right ) = x^{4} {y^{\prime }}^{2}
\] |
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\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }-x^{2} = 0
\] |
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\[
{}{y^{\prime }}^{4} = 4 y \left (x y^{\prime }-2 y\right )^{2}
\] |
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\[
{}\left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\] |
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