Internal problem ID [4171]
Book: Differential Gleichungen, Kamke, 3rd ed, Abel ODEs
Section: Abel ODE’s with constant invariant
Problem number: problem 146.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }+x y^{3}+a y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 82
dsolve(x^2*diff(y(x),x)+x*y(x)^3+a*y(x)^2 = 0,y(x), singsol=all)
\[ c_{1}+\left (x +\frac {a \sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {\sqrt {2}\, \left (a y \relax (x )+x \right )}{2 y \relax (x ) x}\right ) {\mathrm e}^{\frac {\left (a y \relax (x )+x \right )^{2}}{2 y \relax (x )^{2} x^{2}}}}{2}\right ) {\mathrm e}^{-\frac {\left (\left (a +x \right ) y \relax (x )+x \right ) \left (\left (-x +a \right ) y \relax (x )+x \right )}{2 y \relax (x )^{2} x^{2}}} = 0 \]
✓ Solution by Mathematica
Time used: 0.592 (sec). Leaf size: 78
DSolve[x^2*y'[x]+x*y[x]^3+a*y[x]^2 == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {i a}{x}=\frac {2 e^{\frac {1}{2} \left (-\frac {i a}{x}-\frac {i}{y(x)}\right )^2}}{\sqrt {2 \pi } \text {Erfi}\left (\frac {-\frac {i a}{x}-\frac {i}{y(x)}}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]