Find the particular solution of the differential equation that satisfies the initial condition(s). f ′(s) = 14s − 4s3, f(3) = 7

Answer 1

f'(s) = 14s - 4s³

f(s) = ∫f'(s) ds = 7s² - s⁴ + c

f(3) = 7(3)² - 3⁴ + c= 7(9) - 81 + c = 63 - 81 + c = c - 18 = 7

c = 18 + 7 = 25 so f(s) = 7s² - s⁴ + 25