Internal problem ID [7692]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 111.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
Solve \begin {gather*} \boxed {y^{\prime } x +y^{3}+3 x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 54
dsolve(x*diff(y(x),x) + y(x)^3 + 3*x*y(x)^2=0,y(x), singsol=all)
\[ c_{1}-\frac {i {\mathrm e}^{\frac {\left (3 x y \relax (x )-1\right )^{2}}{2 y \relax (x )^{2}}}}{3 x}+\frac {\erf \left (\frac {\left (-i+3 i y \relax (x ) x \right ) \sqrt {2}}{2 y \relax (x )}\right ) \sqrt {2}\, \sqrt {\pi }}{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.345 (sec). Leaf size: 55
DSolve[x*y'[x] + y[x]^3 + 3*x*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [-3 x=\frac {2 e^{\frac {1}{2} \left (\frac {1}{y(x)}-3 x\right )^2}}{\sqrt {2 \pi } \operatorname {Erfi}\left (\frac {\frac {1}{y(x)}-3 x}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]