Hi, here is my problem : I am trying to solve a partial differential equation, which I turned in an ordinary differential equation using this reduction
X:=kx+wt+c
And now my equation is simply, after a first integration :
eqn:=(k^3)u''[X]+wu[X]-2k(u[X]^3)==0
And my problem appears when I use DSolve on this equation, because I want my independent variable to be the funtion itself, then solve for its first derivative.
DSolve[eqn, u'[u[X]], u[X]]
I tried using this instead but it did not work either because I could not find a command that did what I want (but I am just showing you so you can figure out what I want to do) :
Assuming[u[X] -> variable, {DSolve[eqn, u'[u[X]], u[X]]}]
Can you help me with this ?
Thank you