60.7.53 problem 1643 (6.53)

Internal problem ID [11642]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1643 (6.53)
Date solved : Monday, January 27, 2025 at 11:28:57 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }+\phi \left (y\right ) {y^{\prime }}^{2}+f \left (x \right ) y^{\prime }+g \left (x \right ) \Phi \left (y\right )&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x$2)+phi(y(x))*diff(y(x),x)^2+f(x)*diff(y(x),x)+g(x)*Phi(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}]+\[Phi][y[x]]*D[y[x],x]^2+f[x]*D[y[x],x]+g[x]*\[CurlyPhi][y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved