Initial Value Problem

Question

Solve the initial value problem:

ds/dt = 2t + 9t^2

s(1) = 2

Answer 1

s(t) = ∫(9t² + 2t)dt = 3t³ + t² + C

2 = 3(1)³ + (1)² + C

Solve for C:

C = 2 − 3 − 1 = -2

s(t) = 3t³ + t² − 2

The initial value is when t = 0

s(0) = -2