Internal problem ID [3633]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 905.
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: 0.016 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x)^2+3*x*diff(y(x),x)*y(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: 0.042 (sec). Leaf size: 26
DSolve[x^2 (y'[x])^2+3 x y[x] y'[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*}