Internal problem ID [8153]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 573.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {f \left (x \left (y^{\prime }\right )^{2}\right )+2 x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 24
dsolve(f(x*diff(y(x),x)^2)+2*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+2 \sqrt {x}\, \RootOf \left (-f \left (\textit {\_Z}^{2}\right )-2 \textit {\_Z} +c_{1}+c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.495 (sec). Leaf size: 48
DSolve[f[x*y'[x]^2] - y[x] + 2*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to f(c_1)-2 \sqrt {c_1} \sqrt {x} \\ y(x)\to f(c_1)+2 \sqrt {c_1} \sqrt {x} \\ y(x)\to f(0) \\ \end{align*}