60.7.38 problem 1628 (6.38)

Internal problem ID [11627]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1628 (6.38)
Date solved : Monday, January 27, 2025 at 11:27:50 PM
CAS classification : [NONE]

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

✗ Solution by Maple

dsolve(diff(diff(y(x),x),x)+3*y(x)*diff(y(x),x)+y(x)^3+f(x)*y(x)-g(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[-g[x] + f[x]*y[x] + y[x]^3 + 3*y[x]*D[y[x],x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved