Let f'''(t) = 5 t + 10 \sqrt{t}.

Question

(a) Find the most general formula for f''(t). If an arbitrary constant must be used here, use an upper-case "C".

f''(t) =

(b) Based on your answer to (a), find the most general formula for f'(t). If another new arbitrary constant must be used here, use an upper-case "D".

f'(t) =
(c) Based on your answer to (b), find the most general formula for f(t). If another new arbitrary constant must be used here, use an upper-case "E".

f(t) =

Answer 1

I guess you mean
d^3y/dt^3 = 5 t + 10 t^-(1/2)

d^2y/dt^2 = (5/2)t^2 + (20/3)t^(3/2) + C

dy/dt = (5/6)t^3 + (40/15)t^(5/2) +C t+D

and so forth