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ODE |
Mathematica |
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\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+x y \left (y^{2}+x y+x^{2}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
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\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6} = 0
\] |
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\[
{}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\] |
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\[
{}2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
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\[
{}3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y = 0
\] |
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\[
{}4 {y^{\prime }}^{3}+4 y^{\prime } = x
\] |
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\[
{}8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y
\] |
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\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0
\] |
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\[
{}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0
\] |
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\[
{}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\] |
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\[
{}2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x = 0
\] |
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\[
{}4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y = 0
\] |
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\[
{}8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0
\] |
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\[
{}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{\prime } y^{2}+1 = 0
\] |
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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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\[
{}x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2} x^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0
\] |
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\[
{}2 x^{3} {y^{\prime }}^{3}+6 y {y^{\prime }}^{2} x^{2}-\left (1-6 x y\right ) y y^{\prime }+2 y^{3} = 0
\] |
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\[
{}{y^{\prime }}^{3} x^{4}-y {y^{\prime }}^{2} x^{3}-y^{2} y^{\prime } x^{2}+x y^{3} = 1
\] |
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\[
{}x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0
\] |
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\[
{}y {y^{\prime }}^{3}-3 x y^{\prime }+3 y = 0
\] |
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\[
{}2 y {y^{\prime }}^{3}-3 x y^{\prime }+2 y = 0
\] |
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\[
{}\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (y+2 x \right ) y^{\prime } = 0
\] |
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\[
{}y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0
\] |
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\[
{}y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
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\[
{}4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0
\] |
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\[
{}16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
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\[
{}x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0
\] |
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\[
{}y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2} = 0
\] |
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\[
{}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\] |
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\[
{}{y^{\prime }}^{4} = \left (y-a \right )^{3} \left (y-b \right )^{2}
\] |
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\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2} = 0
\] |
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\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} = 0
\] |
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\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2} = 0
\] |
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\[
{}{y^{\prime }}^{4}+x y^{\prime }-3 y = 0
\] |
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\[
{}{y^{\prime }}^{4}-4 y {y^{\prime }}^{2} x^{2}+16 y^{2} y^{\prime } x -16 y^{3} = 0
\] |
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\[
{}{y^{\prime }}^{4}+4 y {y^{\prime }}^{3}+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y = 0
\] |
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\[
{}2 {y^{\prime }}^{4}-y y^{\prime }-2 = 0
\] |
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\[
{}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0
\] |
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\[
{}3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0
\] |
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\[
{}{y^{\prime }}^{6} = \left (y-a \right )^{4} \left (y-b \right )^{3}
\] |
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\[
{}{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3} = 0
\] |
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\[
{}{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3} = 0
\] |
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\[
{}{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4} = 0
\] |
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\[
{}x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2}
\] |
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\[
{}2 \sqrt {a y^{\prime }}+x y^{\prime }-y = 0
\] |
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\[
{}\left (x -y\right ) \sqrt {y^{\prime }} = a \left (1+y^{\prime }\right )
\] |
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\[
{}2 \left (1+y\right )^{{3}/{2}}+3 x y^{\prime }-3 y = 0
\] |
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\[
{}\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } = x
\] |
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\[
{}\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } = y
\] |
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\[
{}\sqrt {1+{y^{\prime }}^{2}} = x y^{\prime }
\] |
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\[
{}\sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+x y^{\prime }-y = 0
\] |
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\[
{}a \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0
\] |
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\[
{}a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0
\] |
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\[
{}\sqrt {\left (a \,x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )}-y y^{\prime }-a x = 0
\] |
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\[
{}a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+x y^{\prime }-y = 0
\] |
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\[
{}\cos \left (y^{\prime }\right )+x y^{\prime } = y
\] |
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\[
{}a \cos \left (y^{\prime }\right )+b y^{\prime }+x = 0
\] |
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\[
{}\sin \left (y^{\prime }\right )+y^{\prime } = x
\] |
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\[
{}y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right ) = y
\] |
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\[
{}{y^{\prime }}^{2} \left (x +\sin \left (y^{\prime }\right )\right ) = y
\] |
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\[
{}\left (1+{y^{\prime }}^{2}\right ) \sin \left (x y^{\prime }-y\right )^{2} = 1
\] |
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\[
{}\left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime } = 0
\] |
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\[
{}{\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}\ln \left (y^{\prime }\right )+x y^{\prime }+a = 0
\] |
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\[
{}\ln \left (y^{\prime }\right )+x y^{\prime }+a = y
\] |
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\[
{}\ln \left (y^{\prime }\right )+x y^{\prime }+a +b y = 0
\] |
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\[
{}\ln \left (y^{\prime }\right )+4 x y^{\prime }-2 y = 0
\] |
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\[
{}\ln \left (y^{\prime }\right )+a \left (x y^{\prime }-y\right ) = 0
\] |
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\[
{}a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y = 0
\] |
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\[
{}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0
\] |
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\[
{}y^{\prime } \ln \left (y^{\prime }\right )-\left (1+x \right ) y^{\prime }+y = 0
\] |
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\[
{}y^{\prime } \ln \left (y^{\prime }+\sqrt {a +{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y = 0
\] |
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\[
{}\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y
\] |
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\[
{}y^{\prime } = \frac {x y}{x^{2}-y^{2}}
\] |
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\[
{}y^{\prime } = \frac {x +y-3}{-y+x -1}
\] |
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\[
{}y^{\prime } = \frac {2 x +y-1}{4 x +2 y+5}
\] |
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\[
{}y^{\prime }-\frac {2 y}{1+x} = \left (1+x \right )^{2}
\] |
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\[
{}y^{\prime }+x y = x^{3} y^{3}
\] |
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\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
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\[
{}y+x y^{2}-x y^{\prime } = 0
\] |
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\[
{}y^{2} \left (1+{y^{\prime }}^{2}\right ) = R^{2}
\] |
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\[
{}y = x y^{\prime }+\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}
\] |
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\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
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\[
{}\left (1+x \right ) y+\left (1-y\right ) x y^{\prime } = 0
\] |
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\[
{}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\] |
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\[
{}x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2} = 0
\] |
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\[
{}1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 0
\] |
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\[
{}\sin \left (x \right ) \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
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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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\[
{}\left (y-x \right ) y^{\prime }+y = 0
\] |
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\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
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\[
{}x y^{\prime }-y-\sqrt {x^{2}+y^{2}} = 0
\] |
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\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
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\[
{}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0
\] |
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\[
{}2 x -y+1+\left (2 y-1\right ) y^{\prime } = 0
\] |
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\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{2 x \left (x^{2}+1\right )}
\] |
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\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
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\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
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\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
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