Internal problem ID [12148]
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`]]
\[ \boxed {y-2 y^{\prime } x -\frac {{y^{\prime }}^{2}}{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 79
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 {1}{2} x^{2}+c_{1} x +\frac {1}{2} c_{1}^{2} \\ y \left (x \right ) &= -\frac {1}{2} x^{2}-c_{1} x +\frac {1}{2} c_{1}^{2} \\ y \left (x \right ) &= -\frac {1}{2} x^{2}-c_{1} x +\frac {1}{2} c_{1}^{2} \\ y \left (x \right ) &= -\frac {1}{2} x^{2}+c_{1} x +\frac {1}{2} c_{1}^{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