Find the particular solution of the differential equation that satisfies the initial condition(s).

Question

f ''(x) = x^−3/2,    f '(4) = 1,    f(0) = 0

f(x) = ?

Answer 1

f'(x) = - 2x^-1/2 + C; f'(4) = - 2/2 + C = 1; C = 2; f'(x) = - 2x^-1/2 + 2;

f(x) = - 4x^1/2 + 2x + D; f(0) = D = 0; D = 0; f(x) = - 4x^1/2 + 2x

Answer 2