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Question: how to program this in maple

Question:how to program this in maple

Lonely 400
integral-equation
March 03 2011
0

 

sorry for posting the same question again. reason: the equation no. (2)

 

Thank you so very much for your help.

 

I was to solve, means find y as a function of x, equations like the following

 

y(x) = 7/8 * x + 1/2 * int (x*t*y(t)^2,t=0..1)

or

y(x):=7/(8)*x+1/(2)*int(x*t*y(t)^(2),t=0..1)

 

To solve above, I need to program the following

 

1. Define

H(u,p):=(1-p)*(7/(8)*x-u)+p*(7/(8)*x+1/(2)*int(x*t*u(t)^(2),t=0..1)-u)

2. Now, I will assume a solution

u := sum(u[i]*p^i, i = 0 .. n)

3. Now we will substitute the equation (2) in the equation (1) {please do it for me and thank you}

4. Now we will set

H(u,p) =0

and equate the like powers of p on both the side of this equation. This will give us various equations. Upon solving these equations we will obtain u_i.

 

5. Substituting these values of u_i in equation (2) gives us our solution.

 

Please help me in programmin this.

Thank you so much.
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