Internal problem ID [8152]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 572.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [x=_G(y,y')]
Solve \begin {gather*} \boxed {\left (x y^{\prime }-y\right )^{n} f \left (y^{\prime }\right )+y g \left (y^{\prime }\right )+x h \left (y^{\prime }\right )=0} \end {gather*}
✗ Solution by Maple
dsolve((x*diff(y(x),x)-y(x))^n*f(diff(y(x),x))+y(x)*g(diff(y(x),x))+x*h(diff(y(x),x))=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x*h[y'[x]] + g[y'[x]]*y[x] + f[y'[x]]*(-y[x] + x*y'[x])^n==0,y[x],x,IncludeSingularSolutions -> True]
Not solved