Internal problem ID [9950]
Internal file name [OUTPUT/8897_Monday_June_06_2022_05_47_44_AM_20255427/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1628 (6.38).
ODE order: 2.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[NONE]
Unable to solve or complete the solution.
\[ \boxed {y^{\prime \prime }+3 y^{\prime } y+y^{3}+f \left (x \right ) y=g \left (x \right )} \]
Maple trace
`Methods for second order ODEs: --- Trying classification methods --- trying 2nd order Liouville trying 2nd order WeierstrassP trying 2nd order JacobiSN differential order: 2; trying a linearization to 3rd order -> Calling odsolve with the ODE`, diff(diff(diff(y(x), x), x), x) = g(x)*y(x)-(diff(y(x), x))*f(x), y(x)` *** Sublevel 2 *** Methods for third order ODEs:`
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[-g[x] + f[x]*y[x] + y[x]^3 + 3*y[x]*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved