Solve the following initial value problem:

Question

dr/dt=7cos(pi(t)), r(1/4)=14

r(t)=?

Answer 1

dr/dt = 7cos πt
r = 7/π sin πt + c

14 = 7/π sin π/4 + c
14 = 7/(π√2) + c
c = 14 - 7/(π√2)

r = 7/π sin πt + 14 - 7/(π√2)