Internal problem ID [8017]
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]
\[ \boxed {x^{2} {y^{\prime }}^{2}+3 y x y^{\prime }+2 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) = \frac {c_{1}}{x} \\ y \left (x \right ) = \frac {c_{1}}{x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.044 (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*}