Internal problem ID [9254]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1676 (book 6.85).
ODE order: 2.
ODE degree: -1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+\left (a +1\right ) x y^{\prime }-x^{k} f \left (x^{k} y, y^{\prime } x +k y\right )=0} \end {gather*}
✗ Solution by Maple
dsolve(x^2*diff(diff(y(x),x),x)+(a+1)*x*diff(y(x),x)-x^k*f(x^k*y(x),x*diff(y(x),x)+k*y(x))=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(x^k*f[x^k*y[x], k*y[x] + x*y'[x]]) + (1 + a)*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved