Internal problem ID [8018]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 438.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}+3 y y^{\prime } x +2 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x)^2+3*x*y(x)*diff(y(x),x)+2*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {c_{1}}{x} \\ y \relax (x ) = \frac {c_{1}}{x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 26
DSolve[2*y[x]^2 + 3*x*y[x]*y'[x] + x^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{x^2} \\ y(x)\to \frac {c_1}{x} \\ y(x)\to 0 \\ \end{align*}