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ODE |
Mathematica |
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\[
{} y^{2} \left (y-x y^{\prime }\right ) = x^{4} {y^{\prime }}^{2}
\]
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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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\[
{} y+x^{2} = {y^{\prime }}^{2}
\]
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\[
{} {y^{\prime }}^{3} = y^{4} \left (x y^{\prime }+y\right )
\]
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\[
{} \left (1-y^{\prime }\right )^{2}-{\mathrm e}^{-2 y} = {y^{\prime }}^{2} {\mathrm e}^{-2 x}
\]
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\[
{} a x y {y^{\prime }}^{2}+\left (x^{2}-y^{2} a -b \right ) y^{\prime }-x y = 0
\]
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\[
{} {y^{\prime }}^{2} = \left (4 y+1\right ) \left (y^{\prime }-y\right )
\]
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\[
{} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+b^{2}-y^{2} = 0
\]
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\[
{} x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}-1\right ) y^{\prime }+x y = 0
\]
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\[
{} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-x y = 0
\]
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\[
{} 8 {y^{\prime }}^{3} x = y \left (12 {y^{\prime }}^{2}-9\right )
\]
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\[
{} 4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2} = 0
\]
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\[
{} \left (y^{2}+x^{2} y^{\prime }\right ) \left (x y^{\prime }+y\right ) = \left (1+y^{\prime }\right )^{2}
\]
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\[
{} y-x y^{\prime } = a \left (y^{2}+y^{\prime }\right )
\]
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\[
{} y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right )
\]
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\[
{} \left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right ) = 2 y^{\prime }
\]
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\[
{} y-x y^{\prime } = 0
\]
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\[
{} \cot \left (y\right )-\tan \left (x \right ) y^{\prime } = 0
\]
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\[
{} x^{3}+x y^{2}+a^{2} y+\left (y^{3}+x^{2} y-a^{2} x \right ) y^{\prime } = 0
\]
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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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\[
{} y \sin \left (x \right )+y^{\prime } \cos \left (x \right ) = 1
\]
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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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\[
{} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\]
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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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\[
{} y+\frac {y^{3}}{3}+\frac {x^{2}}{2}+\frac {\left (x +x y^{2}\right ) y^{\prime }}{4} = 0
\]
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\[
{} 3 x^{2} y^{4}+2 x y+\left (2 x^{3} y^{2}-x^{2}\right ) y^{\prime } = 0
\]
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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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\[
{} {y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\]
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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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\[
{} {y^{\prime }}^{3} \left (x +2 y\right )+3 {y^{\prime }}^{2} \left (x +y\right )+\left (y+2 x \right ) y^{\prime } = 0
\]
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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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\[
{} x^{2} \left (y-x y^{\prime }\right ) = y {y^{\prime }}^{2}
\]
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\[
{} x y \left (y-x y^{\prime }\right ) = x +y y^{\prime }
\]
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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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\[
{} \left (1+{y^{\prime }}^{2}\right ) y^{2} = r^{2}
\]
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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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\[
{} 4 {y^{\prime }}^{2} x = \left (3 x -a \right )^{2}
\]
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\[
{} 4 {y^{\prime }}^{2} x \left (-a +x \right ) \left (x -b \right ) = \left (3 x^{2}-2 x \left (a +b \right )+a b \right )^{2}
\]
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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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\[
{} {y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0
\]
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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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\[
{} \left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (x^{2}+2 x y+y^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\]
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