Internal problem ID [6027]
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: 14.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y \left (y^{\prime }\right )^{2} x +\left (y^{2} x -1\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 34
dsolve(x*y(x)*diff(y(x),x)^2+(x*y(x)^2-1)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {2 \ln \relax (x )+c_{1}} \\ y \relax (x ) = -\sqrt {2 \ln \relax (x )+c_{1}} \\ y \relax (x ) = {\mathrm e}^{-x} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.171 (sec). Leaf size: 57
DSolve[x*y[x]*(y'[x])^2+(x*y[x]^2-1)*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x} \\ y(x)\to -\sqrt {2} \sqrt {\log (x)+c_1} \\ y(x)\to \sqrt {2} \sqrt {\log (x)+c_1} \\ y(x)\to 0 \\ \end{align*}