Find the particular solution y = f(x) that satisfies the differential equation and initial condition.

Question

f '(x) = (3x − 5)(3x + 5),    f(3) = 0

Answer 1

f(x) = ∫f'(x)dx = ∫[9x² - 25]dx = 3x³ - 25x + C

Since f(3) = 0, we have 81 - 75 + C = 0. So, C = -6

Therefore, f(x) = 3x³ - 25x - 6