Internal problem ID [9202]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1623 (6.33).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (y+3 f \relax (x )\right ) y^{\prime }-y^{3}+y^{2} f \relax (x )+y \left (f^{\prime }\relax (x )+2 f \relax (x )^{2}\right )=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)+(y(x)+3*f(x))*diff(y(x),x)-y(x)^3+y(x)^2*f(x)+y(x)*(diff(f(x),x)+2*f(x)^2)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[f[x]*y[x]^2 - y[x]^3 + y[x]*(2*f[x]^2 + Derivative[1][f][x]) + (3*f[x] + y[x])*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved