60.7.52 problem 1642 (6.52)

Internal problem ID [11641]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1642 (6.52)
Date solved : Monday, January 27, 2025 at 11:28:56 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }-\frac {D\left (f \right )\left (y\right ) {y^{\prime }}^{3}}{f \left (y\right )}+g \left (x \right ) y^{\prime }+h \left (x \right ) f \left (y\right )&=0 \end{align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved