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ODE |
Mathematica |
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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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\[
{}2 y^{2} x^{3}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime } = 0
\] |
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\[
{}\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right )+\sqrt {1+x^{2}+y^{2}}\, \left (-x y^{\prime }+y\right ) = 0
\] |
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\[
{}1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
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\[
{}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0
\] |
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\[
{}y^{4} x^{3}+x^{2} y^{3}+x y^{2}+y+\left (y^{3} x^{4}-y^{2} x^{3}-x^{3} y+x \right ) y^{\prime } = 0
\] |
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\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
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\[
{}{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+x y = 0
\] |
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\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
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\[
{}y^{2}+{y^{\prime }}^{2} = 1
\] |
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\[
{}\left (2 x y^{\prime }-y\right )^{2} = 8 x^{3}
\] |
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\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2} = 1
\] |
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\[
{}{y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-y^{2} \left (x^{2}-y^{2}\right ) = 0
\] |
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\[
{}2 x y^{\prime }-y+\ln \left (y^{\prime }\right ) = 0
\] |
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\[
{}4 x {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
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\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
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\[
{}y^{\prime }+2 x y = x^{2}+y^{2}
\] |
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\[
{}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\] |
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\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
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\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
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\[
{}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
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\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
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\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
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\[
{}\left (x y^{\prime }-y\right )^{2} = 1+{y^{\prime }}^{2}
\] |
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\[
{}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0
\] |
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\[
{}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x} = 0
\] |
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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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\[
{}x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x = 0
\] |
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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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\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
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\[
{}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
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\[
{}\left (x -y^{\prime }-y\right )^{2} = x^{2} \left (2 x y-x^{2} y^{\prime }\right )
\] |
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\[
{}y^{2} \left (1+{y^{\prime }}^{2}\right ) = a^{2}
\] |
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\[
{}y y^{\prime } = \left (x -b \right ) {y^{\prime }}^{2}+a
\] |
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\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1 = 0
\] |
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\[
{}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0
\] |
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\[
{}y = {y^{\prime }}^{2} \left (1+x \right )
\] |
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\[
{}\left (x y^{\prime }-y\right ) \left (x +y y^{\prime }\right ) = a^{2} y^{\prime }
\] |
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\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
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\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\] |
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\[
{}x^{2} {y^{\prime }}^{2}-2 \left (x y+2 y^{\prime }\right ) y^{\prime }+y^{2} = 0
\] |
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\[
{}y = x y^{\prime }+\frac {y {y^{\prime }}^{2}}{x^{2}}
\] |
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\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = x^{2} y^{2}+x^{4}
\] |
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\[
{}y = x y^{\prime }+\frac {1}{y^{\prime }}
\] |
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\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
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\[
{}x^{2} {y^{\prime }}^{2}-2 \left (-2+x y\right ) y^{\prime }+y^{2} = 0
\] |
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\[
{}x^{2} {y^{\prime }}^{2}-\left (x -1\right )^{2} = 0
\] |
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\[
{}8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}
\] |
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\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
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\[
{}y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\] |
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\[
{}x^{\prime } = \frac {2 x}{t}
\] |
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\[
{}x^{\prime } = -\frac {t}{x}
\] |
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\[
{}x^{\prime } = -x^{2}
\] |
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\[
{}x^{\prime } = {\mathrm e}^{-x}
\] |
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\[
{}x^{\prime }+2 x = t^{2}+4 t +7
\] |
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\[
{}2 t x^{\prime } = x
\] |
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\[
{}x^{\prime } = x \left (1-\frac {x}{4}\right )
\] |
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\[
{}x^{\prime } = x^{2}+t^{2}
\] |
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\[
{}x^{\prime } = t \cos \left (t^{2}\right )
\] |
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\[
{}x^{\prime } = \frac {t +1}{\sqrt {t}}
\] |
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\[
{}x^{\prime } = t \,{\mathrm e}^{-2 t}
\] |
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\[
{}x^{\prime } = \frac {1}{t \ln \left (t \right )}
\] |
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\[
{}\sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right )
\] |
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\[
{}x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}}
\] |
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\[
{}x^{\prime } = \sqrt {x}
\] |
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\[
{}x^{\prime } = {\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime } = 1+y^{2}
\] |
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\[
{}u^{\prime } = \frac {1}{5-2 u}
\] |
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\[
{}x^{\prime } = a x+b
\] |
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\[
{}Q^{\prime } = \frac {Q}{4+Q^{2}}
\] |
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\[
{}x^{\prime } = {\mathrm e}^{x^{2}}
\] |
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\[
{}y^{\prime } = r \left (a -y\right )
\] |
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\[
{}x^{\prime } = \frac {2 x}{t +1}
\] |
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\[
{}\theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right )
\] |
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\[
{}\left (2 u+1\right ) u^{\prime }-t -1 = 0
\] |
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\[
{}R^{\prime } = \left (t +1\right ) \left (1+R^{2}\right )
\] |
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\[
{}y^{\prime }+y+\frac {1}{y} = 0
\] |
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\[
{}\left (t +1\right ) x^{\prime }+x^{2} = 0
\] |
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\[
{}y^{\prime } = \frac {1}{2 y+1}
\] |
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\[
{}x^{\prime } = \left (4 t -x\right )^{2}
\] |
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\[
{}x^{\prime } = 2 t x^{2}
\] |
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\[
{}x^{\prime } = t^{2} {\mathrm e}^{-x}
\] |
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\[
{}x^{\prime } = x \left (4+x\right )
\] |
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\[
{}x^{\prime } = {\mathrm e}^{t +x}
\] |
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\[
{}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right )
\] |
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\[
{}y^{\prime } = t^{2} \tan \left (y\right )
\] |
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\[
{}x^{\prime } = \frac {\left (4+2 t \right ) x}{\ln \left (x\right )}
\] |
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\[
{}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1}
\] |
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\[
{}x^{\prime } = \frac {t^{2}}{1-x^{2}}
\] |
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\[
{}x^{\prime } = 6 t \left (x-1\right )^{{2}/{3}}
\] |
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\[
{}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 t x}
\] |
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\[
{}x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t} = {\mathrm e}^{-t}
\] |
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\[
{}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}}
\] |
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\[
{}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}}
\] |
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\[
{}x^{\prime } = 2 t^{3} x-6
\] |
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\[
{}\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right ) = 0
\] |
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\[
{}x^{\prime } = t -x^{2}
\] |
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\[
{}7 t^{2} x^{\prime } = 3 x-2 t
\] |
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\[
{}x x^{\prime } = 1-t x
\] |
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\[
{}{x^{\prime }}^{2}+t x = \sqrt {t +1}
\] |
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