find a parametric function which we have its expansion?

hello.

I have calculated an integral equation (general goursat problem) with an iteration method. I want to know how could I use MAPLE to derive a function for.

I found the first 4 iteration for function f.

the exact problem is U_xy=2.U.U_x .

U(x,y)=2x on y=x^2+x and U(x,y)=3x^2 on y=0.

I want to find the U function.

y=t^2+t

U₀=2t-3t^2+3x^2

U_n=U₀+int(2*U_n*(U_n)_x)

U_xy is the x and y derivitives of U.