Internal problem ID [8086]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 506.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {x^{2} \left (x y^{2}-1\right ) \left (y^{\prime }\right )^{2}+2 x^{2} y^{2} \left (y-x \right ) y^{\prime }-y^{2} \left (y x^{2}-1\right )=0} \end {gather*}
✗ Solution by Maple
dsolve(x^2*(x*y(x)^2-1)*diff(y(x),x)^2+2*x^2*y(x)^2*(y(x)-x)*diff(y(x),x)-y(x)^2*(x^2*y(x)-1)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(y[x]^2*(-1 + x^2*y[x])) + 2*x^2*y[x]^2*(-x + y[x])*y'[x] + x^2*(-1 + x*y[x]^2)*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
Not solved