Find f.

Question

f ″(x) = 5ex − 8 sin(x), f(0) = 3, f (𝜋/2)= 0

Answer 1

f" = 5e^x - 8sinx
f' = 5e^x + 8cosx + c1
f = 5e^x + 8sinx + c1*x + c2
Now use the two conditions to get
5+0+0 c1 + c2 = 3
5e^(π/2) + 8 + π/2 * c1 + c2 = 0
Now solve for c1 and c2.