Internal problem ID [10800]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 51.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {y-x^{2}-2 y^{\prime } x -\frac {{y^{\prime }}^{2}}{2}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 95
dsolve(y(x)=x^2+2*diff(y(x),x)*x+(diff(y(x),x)^2)/2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -x^{2} \\ y \left (x \right ) = -\frac {3 x^{2}}{2}-x \left (-x -c_{1} \right )+\frac {c_{1}^{2}}{2} \\ y \left (x \right ) = -\frac {3 x^{2}}{2}-x \left (-x +c_{1} \right )+\frac {c_{1}^{2}}{2} \\ y \left (x \right ) = -\frac {3 x^{2}}{2}+x \left (x -c_{1} \right )+\frac {c_{1}^{2}}{2} \\ y \left (x \right ) = -\frac {3 x^{2}}{2}+x \left (x +c_{1} \right )+\frac {c_{1}^{2}}{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]==x^2+2*y'[x]*x+(y'[x]^2)/2,y[x],x,IncludeSingularSolutions -> True]
Timed out