Question: algorithm of integration

hi,

i want to solve this equation :

 

f(n+1)(x)=f(n)(x)-int [ (s-x)^2 * ( F"(n)(s)+.5*F(n)(s) ) ds]

 integration is from  -infinity  to  x

with this initial guess   f(0)(x)=A+Bx+C*exp[-x]

i want for example F(4)(x) in terms of A,B,C

 and then calculate A,B and C with this condition

f(0)(4)=0

f'(0)(4)=0

f'(10)(4)=1


please help me

 

thancks

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