Internal problem ID [7888]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 308.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 y^{3} y^{\prime }+x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve(2*y(x)^3*diff(y(x),x)+x*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = -\frac {\sqrt {-2 x^{2}+4 c_{1}}}{2} \\ y \relax (x ) = \frac {\sqrt {-2 x^{2}+4 c_{1}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 53
DSolve[x*y[x]^2 + 2*y[x]^3*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to -\sqrt {-\frac {x^2}{2}+2 c_1} \\ y(x)\to \sqrt {-\frac {x^2}{2}+2 c_1} \\ y(x)\to 0 \\ \end{align*}