Internal problem ID [3703]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 978.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y^{2} \left (y^{\prime }\right )^{2}-2 y^{\prime } y x -x^{2}+2 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.171 (sec). Leaf size: 107
dsolve(y(x)^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)-x^2+2*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x \\ y \relax (x ) = x \\ y \relax (x ) = \sqrt {-2 \sqrt {2}\, x c_{1}-c_{1}^{2}-x^{2}} \\ y \relax (x ) = \sqrt {2 \sqrt {2}\, x c_{1}-c_{1}^{2}-x^{2}} \\ y \relax (x ) = -\sqrt {-2 \sqrt {2}\, x c_{1}-c_{1}^{2}-x^{2}} \\ y \relax (x ) = -\sqrt {2 \sqrt {2}\, x c_{1}-c_{1}^{2}-x^{2}} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]^2 (y'[x])^2-2 x y[x] y'[x]-x^2+2 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
Timed out