Internal problem ID [6016]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES
Page 309
Problem number: 3.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-5 x y y^{\prime }+6 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x)^2-5*x*y(x)*diff(y(x),x)+6*y(x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = x^{3} c_{1} \\ y \relax (x ) = c_{1} x^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 26
DSolve[x^2*(y'[x])^2-5*x*y[x]*y'[x]+6*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x^2 \\ y(x)\to c_1 x^3 \\ y(x)\to 0 \\ \end{align*}