Internal problem ID [7691]
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]
\[ \boxed {y^{\prime } x +y^{3}+3 y^{2} x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
dsolve(x*diff(y(x),x) + y(x)^3 + 3*x*y(x)^2=0,y(x), singsol=all)
\[ c_{1} -\frac {i {\mathrm e}^{\frac {\left (3 x y \left (x \right )-1\right )^{2}}{2 y \left (x \right )^{2}}}}{3 x}+\frac {\operatorname {erf}\left (\frac {i \left (3 x y \left (x \right )-1\right ) \sqrt {2}}{2 y \left (x \right )}\right ) \sqrt {2}\, \sqrt {\pi }}{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.365 (sec). Leaf size: 55
DSolve[x*y'[x] + y[x]^3 + 3*x*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-3 x=\frac {2 e^{\frac {1}{2} \left (\frac {1}{y(x)}-3 x\right )^2}}{\sqrt {2 \pi } \text {erfi}\left (\frac {\frac {1}{y(x)}-3 x}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]