Internal problem ID [5020]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 25.
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 x y y^{\prime }+2 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 15
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 ) = c_{1} x^{2} \\ y \relax (x ) = c_{1} x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 24
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 c_1 x \\ y(x)\to c_1 x^2 \\ y(x)\to 0 \\ \end{align*}