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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} y = -a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}}
\]
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\[
{} 4 y = x^{2}+{y^{\prime }}^{2}
\]
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\[
{} x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\]
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\[
{} y = 2 y^{\prime }+3 {y^{\prime }}^{2}
\]
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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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\[
{} y^{2} = a^{2} \left (1+{y^{\prime }}^{2}\right )
\]
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\[
{} y^{2}+x y y^{\prime }-x^{2} {y^{\prime }}^{2} = 0
\]
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\[
{} y = y {y^{\prime }}^{2}+2 x y^{\prime }
\]
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\[
{} y = \left (1+y^{\prime }\right ) x +{y^{\prime }}^{2}
\]
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\[
{} x^{2} \left (y-x y^{\prime }\right ) = y {y^{\prime }}^{2}
\]
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\[
{} y = x y^{\prime }+\arcsin \left (y^{\prime }\right )
\]
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\[
{} {\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2} = 0
\]
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\[
{} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2} = 0
\]
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\[
{} y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\]
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\[
{} x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{3} y^{\prime }+x^{3}
\]
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\[
{} y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\]
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\[
{} {y^{\prime }}^{2}-9 y^{\prime }+18 = 0
\]
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\[
{} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\]
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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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\[
{} \left (x y^{\prime }-y\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\]
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\[
{} 3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\]
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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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\[
{} \left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\]
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\[
{} y^{2} \left (1-{y^{\prime }}^{2}\right ) = b
\]
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\[
{} \left (x y^{\prime }-y\right ) \left (x +y y^{\prime }\right ) = h^{2} y^{\prime }
\]
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\[
{} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2}
\]
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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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\[
{} x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} = a
\]
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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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\[
{} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0
\]
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\[
{} {y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\]
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\[
{} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\]
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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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\[
{} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = b
\]
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\[
{} y = x y^{\prime }+\frac {m}{y^{\prime }}
\]
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\[
{} y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\]
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\[
{} y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} {y^{\prime }}^{2}+x y^{\prime }-y = 0
\]
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\[
{} x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2}+x^{3} = 0
\]
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\[
{} \left (1+y^{\prime }\right )^{3} = \frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a}
\]
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\[
{} y^{2} \left (1+{y^{\prime }}^{2}\right ) = r^{2}
\]
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\[
{} x {y^{\prime }}^{2}-\left (-a +x \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
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\[
{} a {y^{\prime }}^{3} = 27 y
\]
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\[
{} x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\]
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\[
{} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3} = 0
\]
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\[
{} y^{2}-2 x y y^{\prime }+\left (x^{2}-1\right ) {y^{\prime }}^{2} = m^{2}
\]
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\[
{} y = x y^{\prime }+\sqrt {b^{2}+a^{2} y^{\prime }}
\]
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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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\[
{} \left (8 {y^{\prime }}^{3}-27\right ) x = 12 y {y^{\prime }}^{2}
\]
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\[
{} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-b^{2} = 0
\]
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\[
{} \left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right ) = 2 y^{\prime }
\]
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\[
{} \frac {x +y y^{\prime }}{x y^{\prime }-y} = \sqrt {\frac {a^{2}-x^{2}-y^{2}}{x^{2}+y^{2}}}
\]
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\[
{} {x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right )
\]
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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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\[
{} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right ) = y^{2}
\]
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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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\[
{} x +y {y^{\prime }}^{2} = y^{\prime } \left (1+x y\right )
\]
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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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\[
{} \left (y^{\prime }+y+x \right ) \left (x y^{\prime }+y+x \right ) \left (y^{\prime }+2 x \right ) = 0
\]
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\[
{} x^{2} {y^{\prime }}^{3}+y \left (1+x^{2} y\right ) {y^{\prime }}^{2}+y^{2} y^{\prime } = 0
\]
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\[
{} x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\]
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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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\[
{} y = y^{\prime } \tan \left (y^{\prime }\right )+\ln \left (\cos \left (y^{\prime }\right )\right )
\]
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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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\[
{} \left (y-x y^{\prime }\right ) \left (y^{\prime }-1\right ) = y^{\prime }
\]
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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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