Internal problem ID [6885]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th
edition. 1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 24.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x*diff(y(x),x)^2+y(x)*(1-x)*diff(y(x),x)-y(x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {c_{1}}{x} y \left (x \right ) = {\mathrm e}^{x} c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 26
DSolve[x*y'[x]^2+y[x]*(1-x)*y'[x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x y(x)\to \frac {c_1}{x} y(x)\to 0 \end{align*}