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ODE |
Mathematica |
Maple |
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\[
{} \left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime } = \left (1+y^{2}\right )^{{3}/{2}}
\]
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\[
{} y^{\prime } \left (x^{2}+y^{2}+3\right ) = 2 x \left (2 y-\frac {x^{2}}{y}\right )
\]
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\[
{} y^{\prime } = y^{2}-x^{2}
\]
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\[
{} \frac {x +y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y-x y^{\prime }}{x^{2}+y^{2}} = 0
\]
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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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\[
{} \frac {\sin \left (\frac {x}{y}\right )}{y}-\frac {y \cos \left (\frac {y}{x}\right )}{x^{2}}+1+\left (\frac {\cos \left (\frac {y}{x}\right )}{x}-\frac {x \sin \left (\frac {x}{y}\right )}{y^{2}}+\frac {1}{y^{2}}\right ) y^{\prime } = 0
\]
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\[
{} \frac {1}{x}-\frac {y^{2}}{\left (x -y\right )^{2}}+\left (\frac {x^{2}}{\left (x -y\right )^{2}}-\frac {1}{y}\right ) y^{\prime } = 0
\]
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\[
{} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0
\]
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\[
{} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0
\]
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\[
{} 2 x^{3}+3 x^{2} y+y^{2}-y^{3}+\left (2 y^{3}+3 x y^{2}+x^{2}-x^{3}\right ) y^{\prime } = 0
\]
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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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\[
{} {y^{\prime }}^{3}-x^{3} \left (1-y^{\prime }\right ) = 0
\]
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\[
{} {y^{\prime }}^{4} = 4 y \left (x y^{\prime }-2 y\right )^{2}
\]
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\[
{} y = \frac {k \left (x +y y^{\prime }\right )}{\sqrt {1+{y^{\prime }}^{2}}}
\]
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\[
{} x = y y^{\prime }+a {y^{\prime }}^{2}
\]
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\[
{} y = x {y^{\prime }}^{2}+{y^{\prime }}^{3}
\]
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\[
{} y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\]
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\[
{} {y^{\prime }}^{2} \left (x^{2}-1\right )-2 x y y^{\prime }+y^{2}-1 = 0
\]
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\[
{} {y^{\prime }}^{2}+2 x y^{\prime }+2 y = 0
\]
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\[
{} {y^{\prime }}^{4} = 4 y \left (x y^{\prime }-2 y\right )^{2}
\]
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\[
{} y = {y^{\prime }}^{2}-x y^{\prime }+\frac {x^{3}}{2}
\]
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\[
{} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0
\]
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\[
{} y^{\prime \prime } = \frac {1}{\sqrt {y}}
\]
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\[
{} a^{3} y^{\prime \prime \prime } y^{\prime \prime } = \sqrt {1+c^{2} {y^{\prime \prime }}^{2}}
\]
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\[
{} 2 \left (2 a -y\right ) y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3} = 0
\]
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\[
{} {y^{\prime }}^{2}+y y^{\prime \prime } = y^{2} \ln \left (y\right )
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
\]
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\[
{} n \,x^{3} y^{\prime \prime } = \left (y-x y^{\prime }\right )^{2}
\]
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\[
{} y^{2} \left (x^{2} y^{\prime \prime }-x y^{\prime }+y\right ) = x^{3}
\]
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\[
{} x^{2} y^{2} y^{\prime \prime }-3 x y^{2} y^{\prime }+4 y^{3}+x^{6} = 0
\]
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\[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
\]
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\[
{} x \left (x^{2} y^{\prime }+2 x y\right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 x y y^{\prime }+4 y^{2}-1 = 0
\]
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\[
{} x \left (1+x y\right ) y^{\prime \prime }+x^{2} {y^{\prime }}^{2}+\left (4 x y+2\right ) y^{\prime }+y^{2}+1 = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-{y^{\prime }}^{4} = 0
\]
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\[
{} a^{2} y^{\prime \prime } = 2 x \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 x y y^{\prime } = 4 y^{2}
\]
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\[
{} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime } = 0
\]
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\[
{} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )} = 0
\]
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\[
{} {y^{\prime \prime }}^{2}+2 x y^{\prime \prime }-y^{\prime } = 0
\]
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\[
{} {y^{\prime \prime }}^{2}-2 x y^{\prime \prime }-y^{\prime } = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime } = 2 y
\]
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\[
{} x y^{\prime \prime \prime }-y^{\prime \prime }+x y^{\prime }-y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = x -1
\]
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\[
{} \left (x^{2}+2\right ) y^{\prime \prime \prime }-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }-2 x y = x^{4}+12
\]
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\[
{} y^{\prime \prime }+\frac {y}{\ln \left (x \right ) x^{2}} = {\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right )
\]
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\[
{} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime }+\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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\[
{} y^{\prime \prime }+\frac {2 p y^{\prime }}{x}+y = 0
\]
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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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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0
\]
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\[
{} \left [y^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {y \left (x \right )}{2}\right ]
\]
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\[
{} \left [y^{\prime }\left (x \right ) = 1-\frac {1}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {1}{y \left (x \right )-x}\right ]
\]
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\[
{} y^{\prime \prime } = x +y^{2}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y^{2} = 0
\]
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\[
{} \left [y^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {z \left (x \right )^{2}}{y \left (x \right )}\right ]
\]
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\[
{} \left [y^{\prime }\left (x \right )+\frac {2 z \left (x \right )}{x^{2}} = 1, z^{\prime }\left (x \right )+y \left (x \right ) = x\right ]
\]
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\[
{} x y^{\prime }+y = y^{\prime } \sqrt {1-x^{2} y^{2}}
\]
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\[
{} x y^{\prime } = \sqrt {x^{2}+y^{2}}
\]
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\[
{} y^{\prime } = \frac {x +y-1}{x +4 y+2}
\]
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\[
{} \sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\]
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\[
{} y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0
\]
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\[
{} \left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right )
\]
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\[
{} 2 x y^{3}+\cos \left (x \right ) y+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0
\]
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\[
{} 2 y^{4} x +\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} {\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0
\]
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\[
{} \frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1
\]
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\[
{} \left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\]
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\[
{} x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0
\]
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\[
{} y+\left (x -2 x^{2} y^{3}\right ) y^{\prime } = 0
\]
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\[
{} y \ln \left (y\right )-2 x y+\left (x +y\right ) y^{\prime } = 0
\]
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\[
{} y^{2}+x y+1+\left (x^{2}+x y+1\right ) y^{\prime } = 0
\]
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\[
{} y-x y^{2}+\left (x +x^{2} y^{2}\right ) y^{\prime } = 0
\]
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\[
{} x y^{\prime }-y = x^{2} y^{4} \left (x y^{\prime }+y\right )
\]
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\[
{} y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right )
\]
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\[
{} y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right )
\]
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\[
{} {y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
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\[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = y^{\prime } {\mathrm e}^{y}
\]
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\[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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\[
{} y y^{\prime \prime } = {y^{\prime }}^{2}
\]
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\[
{} x y^{\prime } = \sqrt {x^{2}+y^{2}}
\]
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\[
{} y^{2} = \left (x^{3}-x y\right ) y^{\prime }
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}-2 y y^{\prime } = 0
\]
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\[
{} \left ({\mathrm e}^{x}-3 x^{2} y^{2}\right ) y^{\prime }+y \,{\mathrm e}^{x} = 2 x y^{3}
\]
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\[
{} y^{2} {\mathrm e}^{x y}+\cos \left (x \right )+\left ({\mathrm e}^{x y}+x y \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\]
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\[
{} {\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{x} \cos \left (y\right ) y^{\prime } = y \sin \left (x y\right )+x \sin \left (x y\right ) y^{\prime }
\]
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\[
{} \left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime \prime } = 2 x y-{\mathrm e}^{y}-x
\]
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\[
{} \frac {3 y^{2}}{x^{2}+3 x}+\left (2 y \ln \left (\frac {5 x}{x +3}\right )+3 \sin \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} 3 x^{2} y-y^{3}-\left (3 x y^{2}-x^{3}\right ) y^{\prime } = 0
\]
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\[
{} 3 x^{2} {\mathrm e}^{y}-2 x +\left (x^{3} {\mathrm e}^{y}-\sin \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\]
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\[
{} \frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime } = 0
\]
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