Internal problem ID [12221]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 183.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, _dAlembert]
\[ \boxed {y-x {y^{\prime }}^{2}-{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) = 0 y \left (x \right ) = \frac {x \left (x +1+\sqrt {c_{1} x +c_{1} +x +1}\right )^{2}}{\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 \left (x \right ) = \frac {x \left (-x -1+\sqrt {c_{1} x +c_{1} +x +1}\right )^{2}}{\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: 0.108 (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*}