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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} 3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3} = a \,x^{3}
\]
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\[
{} \left (x +y\right )^{2} y^{\prime } = a^{2}
\]
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\[
{} x y^{\prime }-y = \sqrt {x^{2}+y^{2}}
\]
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\[
{} x y^{\prime }-y = x \sqrt {x^{2}+y^{2}}
\]
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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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\[
{} \left (x^{2}-x^{2} y\right ) y^{\prime }+y^{2}+x y^{2} = 0
\]
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\[
{} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1
\]
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\[
{} 3 y^{\prime }+\frac {2 y}{1+x} = \frac {x^{3}}{y^{2}}
\]
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\[
{} 2 x -y+1+\left (2 y-x -1\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\]
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\[
{} x y^{\prime }+\frac {y^{2}}{x} = y
\]
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\[
{} x \left (x^{2}+y^{2}-a^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime }+\frac {4 x y}{x^{2}+1} = \frac {1}{\left (x^{2}+1\right )^{3}}
\]
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\[
{} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\]
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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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\[
{} x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\]
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\[
{} x +y y^{\prime } = m \left (x y^{\prime }-y\right )
\]
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\[
{} y^{\prime }+\cos \left (x \right ) y = y^{n} \sin \left (2 x \right )
\]
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\[
{} \left (1+x \right ) y^{\prime }+1 = 2 \,{\mathrm e}^{y}
\]
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\[
{} y^{\prime } = x^{3} y^{3}-x y
\]
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\[
{} y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\]
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\[
{} \left (1+6 y^{2}-3 x^{2} y\right ) y^{\prime } = 3 x y^{2}-x^{2}
\]
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\[
{} y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0
\]
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\[
{} \left (x^{2} y^{3}+x y\right ) y^{\prime } = 1
\]
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\[
{} y y^{\prime } = a x
\]
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\[
{} \sqrt {a^{2}+x^{2}}\, y^{\prime }+y = \sqrt {a^{2}+x^{2}}-x
\]
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\[
{} \left (x +y\right ) y^{\prime }+x -y = 0
\]
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\[
{} y y^{\prime }+b y^{2} = a \cos \left (x \right )
\]
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\[
{} 2 x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0
\]
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\[
{} y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right )
\]
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\[
{} 3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0
\]
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\[
{} \left (x^{3} y^{3}+x^{2} y^{2}+x y+1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-x y+1\right ) x y^{\prime } = 0
\]
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\[
{} 2 x^{2} y^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime } = 0
\]
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\[
{} y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\]
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\[
{} y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\]
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\[
{} \left (x -y\right )^{2} y^{\prime } = a^{2}
\]
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\[
{} {y^{\prime }}^{3}+2 {y^{\prime }}^{2} x -y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\]
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\[
{} {y^{\prime }}^{2}-a \,x^{3} = 0
\]
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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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\[
{} {y^{\prime }}^{3} = a \,x^{4}
\]
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\[
{} 4 y^{2} {y^{\prime }}^{2}+2 y^{\prime } x y \left (3 x +1\right )+3 x^{3} = 0
\]
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\[
{} {y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\]
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\[
{} x -y y^{\prime } = a {y^{\prime }}^{2}
\]
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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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\[
{} {y^{\prime }}^{2} x -2 y y^{\prime }+a x = 0
\]
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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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\[
{} y = x \left (1+y^{\prime }\right )+{y^{\prime }}^{2}
\]
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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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\[
{} x y \left (y-x y^{\prime }\right ) = x +y y^{\prime }
\]
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\[
{} y^{\prime }+2 x y = x^{2}+y^{2}
\]
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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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\[
{} x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{\prime } y^{3}+x^{3}
\]
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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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\[
{} {y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\]
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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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\[
{} {y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\]
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\[
{} {y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\]
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\[
{} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{y^{\prime }}^{3} {\mathrm e}^{2 y} = 0
\]
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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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\[
{} y^{\prime } \sqrt {x} = \sqrt {y}
\]
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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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\[
{} \left (1+{y^{\prime }}^{2}\right ) y^{2} = r^{2}
\]
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\[
{} {y^{\prime }}^{2} x -\left (-a +x \right )^{2} = 0
\]
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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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\[
{} {y^{\prime }}^{2} x -2 y y^{\prime }+a x = 0
\]
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\[
{} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3} = 0
\]
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\[
{} y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = m^{2}
\]
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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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