Internal problem ID [8060]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 480.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {\left (a y-x^{2}\right ) \left (y^{\prime }\right )^{2}+2 x y \left (y^{\prime }\right )^{2}-y^{2}=0} \end {gather*}
✗ Solution by Maple
dsolve((a*y(x)-x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)^2-y(x)^2 = 0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-y[x]^2 + 2*x*y[x]*y'[x]^2 + (-x^2 + a*y[x])*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
Not solved