Internal problem ID [9224]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1645 (6.55).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (\left (y^{\prime }\right )^{2}+1\right ) \left (f \left (x , y\right ) y^{\prime }+g \left (x , y\right )\right )=0} \end {gather*}
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[(g[x, y[x]] + f[x, y[x]]*y'[x])*(1 + y'[x]^2) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved