I started solving this DE this way:
y=x^m
y'=m*x^(m-1)
y''=m(m-1)x^(m-2)
y'''=m(m-1)(m-2)x^(m-3)
and replace them in DE we get:
(m-1)(m-2)(m*x^(m-1)-x^m)=0
so we get :
y1=x
y2=x^2
m*x^(m-1)-x^m=0 this is the third solution but i don't know how to find it
thank you.
I can find that first and second obvious solution of the homogeneous part x and x^2,but how can I find the third,it is something of x^x.
Can anyone explain how to find the particular solution showing me some steps of the solution.Thank you