60.7.85 problem 1676 (book 6.85)

Internal problem ID [11674]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1676 (book 6.85)
Date solved : Monday, January 27, 2025 at 11:29:51 PM
CAS classification : [NONE]

\begin{align*} x^{2} y^{\prime \prime }+\left (a +1\right ) x y^{\prime }-x^{k} f \left (x^{k} y, x y^{\prime }+k y\right )&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[-(x^k*f[x^k*y[x], k*y[x] + x*D[y[x],x]]) + (1 + a)*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved