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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} \left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2} = 0
\]
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\[
{} \left (a y^{2}+b x +c \right ) {y^{\prime }}^{2}-b y y^{\prime }+d y^{2} = 0
\]
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\[
{} \left (a y-b x \right )^{2} \left (a^{2} {y^{\prime }}^{2}+b^{2}\right )-c^{2} \left (a y^{\prime }+b \right )^{2} = 0
\]
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\[
{} \left (\operatorname {b2} y+\operatorname {a2} x +\operatorname {c2} \right )^{2} {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {b0} y+\operatorname {a0} +\operatorname {c0} = 0
\]
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\[
{} x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y = 0
\]
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\[
{} x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3} = 0
\]
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\[
{} x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (y-x \right ) y^{\prime }-y^{2} \left (x^{2} y-1\right ) = 0
\]
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\[
{} \left (y^{4}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+y^{2} \left (y^{2}-a^{2}\right ) = 0
\]
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\[
{} \left (y^{4}+x^{2} y^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2} = 0
\]
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\[
{} 9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2} = 0
\]
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\[
{} x^{2} \left (x^{2} y^{4}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (y^{2}-x^{2}\right ) y^{\prime }-y^{2} \left (x^{4} y^{2}-1\right ) = 0
\]
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\[
{} \left (a^{2} \sqrt {x^{2}+y^{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a^{2} \sqrt {x^{2}+y^{2}}-y^{2} = 0
\]
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\[
{} \left (a \left (x^{2}+y^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (x^{2}+y^{2}\right )^{{3}/{2}}-y^{2} = 0
\]
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\[
{} {y^{\prime }}^{2} \sin \left (y\right )+2 x y^{\prime } \cos \left (y\right )^{3}-\sin \left (y\right ) \cos \left (y\right )^{4} = 0
\]
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\[
{} {y^{\prime }}^{2} \left (a \cos \left (y\right )+b \right )-c \cos \left (y\right )+d = 0
\]
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\[
{} f \left (x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} \left (x^{2}+y^{2}\right ) f \left (\frac {x}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} \left (x^{2}+y^{2}\right ) f \left (\frac {y}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (y-a \right )^{2} \left (y-b \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}-f \left (x \right ) \left (a y^{2}+b y+c \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}+y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{3}+x y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (x +5\right ) y^{\prime }+y = 0
\]
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\[
{} {y^{\prime }}^{3}-a x y^{\prime }+x^{3} = 0
\]
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\[
{} {y^{\prime }}^{3}-2 y y^{\prime }+y^{2} = 0
\]
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\[
{} {y^{\prime }}^{2}-a x y y^{\prime }+2 a y^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-y^{3} x^{3} = 0
\]
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\[
{} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0
\]
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\[
{} {y^{\prime }}^{3}+a {y^{\prime }}^{2}+b y+a b x = 0
\]
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\[
{} {y^{\prime }}^{3}+{y^{\prime }}^{2} x -y = 0
\]
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\[
{} {y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2} = 0
\]
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\[
{} {y^{\prime }}^{2}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6} = 0
\]
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\[
{} a {y^{\prime }}^{3}+b {y^{\prime }}^{2}+c y^{\prime }-y-d = 0
\]
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\[
{} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0
\]
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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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\[
{} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{3}+b x \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+y^{\prime }+b x = 0
\]
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\[
{} x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y = 0
\]
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\[
{} 2 \left (x y^{\prime }+y\right )^{3}-y y^{\prime } = 0
\]
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\[
{} {y^{\prime }}^{3} \sin \left (x \right )-\left (y \sin \left (x \right )-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+y \sin \left (x \right ) = 0
\]
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\[
{} 2 {y^{\prime }}^{3} y-y {y^{\prime }}^{2}+2 x y^{\prime }-x = 0
\]
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\[
{} y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\]
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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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\[
{} x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5} = 0
\]
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\[
{} {y^{\prime }}^{4}-\left (y-a \right )^{3} \left (y-b \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{4}+3 \left (x -1\right ) {y^{\prime }}^{2}-3 \left (2 y-1\right ) y^{\prime }+3 x = 0
\]
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\[
{} {y^{\prime }}^{4}-4 y \left (x y^{\prime }-2 y\right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{6}-\left (y-a \right )^{4} \left (y-b \right )^{3} = 0
\]
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\[
{} x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2} = 0
\]
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\[
{} {y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}} = 0
\]
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\[
{} {y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1} = 0
\]
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\[
{} {y^{\prime }}^{n}-f \left (x \right ) g \left (y\right ) = 0
\]
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\[
{} a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y = 0
\]
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\[
{} x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y = 0
\]
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\[
{} \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0
\]
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\[
{} \sqrt {1+{y^{\prime }}^{2}}+{y^{\prime }}^{2} x +y = 0
\]
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\[
{} x \left (\sqrt {1+{y^{\prime }}^{2}}+y^{\prime }\right )-y = 0
\]
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\[
{} a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0
\]
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\[
{} y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x = 0
\]
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\[
{} a y \sqrt {1+{y^{\prime }}^{2}}-2 x y y^{\prime }+y^{2}-x^{2} = 0
\]
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\[
{} f \left (x^{2}+y^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y = 0
\]
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\[
{} a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+b x y^{\prime }-y = 0
\]
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\[
{} \ln \left (y^{\prime }\right )+x y^{\prime }+a y+b = 0
\]
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\[
{} \ln \left (y^{\prime }\right )+a \left (x y^{\prime }-y\right ) = 0
\]
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\[
{} y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0
\]
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\[
{} \sin \left (y^{\prime }\right )+y^{\prime }-x = 0
\]
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\[
{} a \cos \left (y^{\prime }\right )+b y^{\prime }+x = 0
\]
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\[
{} {y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y = 0
\]
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\[
{} \left (1+{y^{\prime }}^{2}\right ) \sin \left (x y^{\prime }-y\right )^{2}-1 = 0
\]
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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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\[
{} a \,x^{n} f \left (y^{\prime }\right )+x y^{\prime }-y = 0
\]
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\[
{} f \left ({y^{\prime }}^{2} x \right )+2 x y^{\prime }-y = 0
\]
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\[
{} f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y = 0
\]
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\[
{} y^{\prime } = F \left (\frac {y}{x +a}\right )
\]
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\[
{} y^{\prime } = 2 x +F \left (y-x^{2}\right )
\]
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\[
{} y^{\prime } = -\frac {a x}{2}+F \left (y+\frac {a \,x^{2}}{4}+\frac {b x}{2}\right )
\]
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\[
{} y^{\prime } = F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x}
\]
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\[
{} y^{\prime } = \frac {1+2 F \left (\frac {4 x^{2} y+1}{4 x^{2}}\right ) x}{2 x^{3}}
\]
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\[
{} y^{\prime } = \frac {1+F \left (\frac {a x y+1}{a x}\right ) a \,x^{2}}{a \,x^{2}}
\]
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\[
{} y^{\prime } = -\frac {\left (a \,x^{2}-2 F \left (y+\frac {a \,x^{4}}{8}\right )\right ) x}{2}
\]
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\[
{} y^{\prime } = \frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a}
\]
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\[
{} y^{\prime } = F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )\right ) y
\]
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\[
{} y^{\prime } = \frac {F \left (\frac {y}{\sqrt {x^{2}+1}}\right ) x}{\sqrt {x^{2}+1}}
\]
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\[
{} y^{\prime } = \frac {\left (x^{{3}/{2}}+2 F \left (y-\frac {x^{3}}{6}\right )\right ) \sqrt {x}}{2}
\]
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\[
{} y^{\prime } = \frac {x +F \left (-\left (x -y\right ) \left (x +y\right )\right )}{y}
\]
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\[
{} y^{\prime } = \frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x}
\]
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\[
{} y^{\prime } = \frac {x}{-y+F \left (x^{2}+y^{2}\right )}
\]
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\[
{} y^{\prime } = \frac {F \left (\frac {a y^{2}+b \,x^{2}}{a}\right ) x}{\sqrt {a}\, y}
\]
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\[
{} y^{\prime } = \frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x}
\]
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\[
{} y^{\prime } = \frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}}
\]
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\[
{} y^{\prime } = \frac {F \left (-\frac {-y^{2}+b}{x^{2}}\right ) x}{y}
\]
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\[
{} y^{\prime } = \frac {F \left (\frac {1+x y^{2}}{x}\right )}{y x^{2}}
\]
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\[
{} y^{\prime } = \frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x}
\]
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\[
{} y^{\prime } = \frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )}
\]
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\[
{} y^{\prime } = \frac {y+F \left (\frac {y}{x}\right )}{x -1}
\]
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\[
{} y^{\prime } = \frac {-x +F \left (x^{2}+y^{2}\right )}{y}
\]
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\[
{} y^{\prime } = \frac {F \left (-\frac {2 y \ln \left (x \right )-1}{y}\right ) y^{2}}{x}
\]
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\[
{} y^{\prime } = \frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y}
\]
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\[
{} y^{\prime } = \frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}}
\]
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