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Question: Solve the Nonlinear ODE

Question:Solve the Nonlinear ODE

mehran rajabi 120 Maple
ode dsolve differential-equations bvp
December 17 2017
0

hi every body: 

i want to solve the below ODE with boundry conditions ics, can anybody help me?

The ODE:

ode := x^3*(diff(f(x), x, x, x, x))+alpha*(x^4*(diff(f(x), x, x))+x^3*(diff(f(x), x, x))-x^2*(diff(f(x), x)))-2*x^2*(diff(f(x), x, x, x))+3*x*(diff(f(x), x, x))-3*(diff(f(x), x))+R*x*f(x)^2-R*x^2*(diff(f(x), x, x))*(diff(f(x), x))-3*R*x*f(x)*(diff(f(x), x, x))+3*R*f(x)*(diff(f(x), x))+x^2*R*f(x)*(diff(f(x), x, x, x))-M^2*(x^3*(diff(f(x), x, x, x))-x^2*(diff(f(x), x))) = 0

The boundry conditions:
ics := f(0) = 0, f(1) = 1, (D(f))(1) = 0, limit(diff((diff(f(x), x))/x, x), x = 0) = 0

M,R,alpha are constants.

with regards... 
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