Internal problem ID [6017]
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: 4.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}+x y^{\prime }-y^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(x^2*diff(y(x),x)^2+x*diff(y(x),x)-y(x)^2-y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x \\ y \relax (x ) = \frac {c_{1}-x}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 31
DSolve[x^2*(y'[x])^2+x*y'[x]-y[x]^2-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x \\ y(x)\to -1+\frac {c_1}{x} \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}