60.7.103 problem 1694 (book 6.103)

Internal problem ID [11692]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1694 (book 6.103)
Date solved : Monday, January 27, 2025 at 11:30:08 PM
CAS classification : [NONE]

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

✗ Solution by Maple

dsolve(f(x)^2*diff(diff(y(x),x),x)+f(x)*diff(f(x),x)*diff(y(x),x)-h(y(x),f(x)*diff(y(x),x))=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[-h[y[x], f[x]*D[y[x],x]] + f[x]*Derivative[1][f][x]*D[y[x],x] + f[x]^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved