Internal problem ID [6018]
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: 5.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(x*diff(y(x),x)^2+(1-x^2*y(x))*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ y \relax (x ) = -\ln \relax (x )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 28
DSolve[x*(y'[x])^2+(1-x^2*y[x])*y'[x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to -\log (x)+c_1 \\ \end{align*}