Internal problem ID [6320]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 30.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class C], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y-x \left (y^{\prime }\right )^{2}-\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.174 (sec). Leaf size: 99
dsolve(y(x)=x*diff(y(x),x)^2+diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \frac {\left (x +1+\sqrt {c_{1} x +c_{1}+x +1}\right )^{2} x}{\left (x +1\right )^{2}}+\frac {\left (x +1+\sqrt {c_{1} x +c_{1}+x +1}\right )^{2}}{\left (x +1\right )^{2}} \\ y \relax (x ) = \frac {\left (-x -1+\sqrt {c_{1} x +c_{1}+x +1}\right )^{2} x}{\left (x +1\right )^{2}}+\frac {\left (-x -1+\sqrt {c_{1} x +c_{1}+x +1}\right )^{2}}{\left (x +1\right )^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 57
DSolve[y[x]==x*(y'[x])^2+(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-c_1 \sqrt {x+1}+1+\frac {c_1{}^2}{4} \\ y(x)\to x+c_1 \sqrt {x+1}+1+\frac {c_1{}^2}{4} \\ y(x)\to 0 \\ \end{align*}