Internal problem ID [8743]
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]
\[ \boxed {x {y^{\prime }}^{2}-y=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 39
dsolve(x*diff(y(x),x)^2-y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \frac {\left (x +\sqrt {x c_{1}}\right )^{2}}{x} y \left (x \right ) = \frac {\left (-x +\sqrt {x c_{1}}\right )^{2}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.05 (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*}