(a) Check if u(x)= cos2x is a solution of the integral equation u(x) = cosx + 3 f k(x, t)u(t)dt, where sint cosx 0stsx k(x,t) = cost sinx x

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Chapter2: Second-order Linear Odes
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please solve part (a) step by step with clear writting so i can understand well.. thank you 

(a)
Check if u(x)= cos2x is a solution of the integral equation
u(x) = cosx + 3 f k(x, t)u(t)dt, where
k(x, t) = { sint cosx
i cost sinx
0stsx
or not.
(b) For what value of 1, the function u(x)=1+ Ax is a solution of the integral equation
x =
ex-t u(t)dt.
Transcribed Image Text:(a) Check if u(x)= cos2x is a solution of the integral equation u(x) = cosx + 3 f k(x, t)u(t)dt, where k(x, t) = { sint cosx i cost sinx 0stsx or not. (b) For what value of 1, the function u(x)=1+ Ax is a solution of the integral equation x = ex-t u(t)dt.
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