60.7.55 problem 1645 (6.55)

Internal problem ID [11644]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1645 (6.55)
Date solved : Monday, January 27, 2025 at 11:28:59 PM
CAS classification : [NONE]

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

✗ Solution by Maple

dsolve(diff(diff(y(x),x),x)+(diff(y(x),x)^2+1)*(f(x,y(x))*diff(y(x),x)+g(x,y(x)))=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved