Internal problem ID [8111]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 531.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) \left (y^{\prime }\right )^{2}+\left (x y^{6}+y^{4} x^{2}+y^{2} x^{3}\right ) y^{\prime }-x^{3} y^{6}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)^2-(y(x)^4+x*y(x)^2+x^2)*diff(y(x),x)^2+(x*y(x)^6+x^2*y(x)^4+x^3*y(x)^2)*diff(y(x),x)-x^3*y(x)^6=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(x^3*y[x]^6) + (x^3*y[x]^2 + x^2*y[x]^4 + x*y[x]^6)*y'[x] + y'[x]^2 - (x^2 + x*y[x]^2 + y[x]^4)*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
Not solved