Internal problem ID [7987]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 407.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.214 (sec). Leaf size: 39
dsolve(x*diff(y(x),x)^2-y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \frac {\left (x +\sqrt {c_{1} x}\right )^{2}}{x} \\ y \relax (x ) = \frac {\left (-x +\sqrt {c_{1} x}\right )^{2}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 46
DSolve[-y[x] + x*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-2 \sqrt {x}+c_1\right ){}^2 \\ y(x)\to \frac {1}{4} \left (2 \sqrt {x}+c_1\right ){}^2 \\ y(x)\to 0 \\ \end{align*}