Internal problem ID [6776]
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: 10.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(y(x)*diff(y(x),x)^2+(x-y(x)^2)*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {-x^{2}+c_{1}} y \left (x \right ) = -\sqrt {-x^{2}+c_{1}} y \left (x \right ) = {\mathrm e}^{x} c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 54
DSolve[y[x]*(y'[x])^2+(x-y[x]^2)*y'[x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x y(x)\to -\sqrt {-x^2+2 c_1} y(x)\to \sqrt {-x^2+2 c_1} y(x)\to 0 \end{align*}