Internal problem ID [8806]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 471.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }=x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(y(x)*diff(y(x),x)^2-(y(x)-x)*diff(y(x),x)-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 ) = c_{1} +x \end{align*}
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 47
DSolve[-x - (-x + y[x])*y'[x] + y[x]*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+c_1 y(x)\to -\sqrt {-x^2+2 c_1} y(x)\to \sqrt {-x^2+2 c_1} \end{align*}