Internal problem ID [7088]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 44.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y-x {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 39
dsolve(y(x)=x*(diff(y(x),x))^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \frac {\left (x +\sqrt {c_{1} x}\right )^{2}}{x} y \left (x \right ) = \frac {\left (-x +\sqrt {c_{1} x}\right )^{2}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 46
DSolve[y[x]==x*(y'[x])^2,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*}