A Level H2 Math - Differential Eqns

Two scientists are investigating the change of a certain population of size n thousand at time t years.

i) One scientist suggests that n and t are related by the differential equation

d^2n/dt^2 = 10 - 6t. Find the general solution given that n= 100 when t= 0.

Ans: -t^3 + 5t^2 + kt +100

i got this:

n = 5t^2 + t^3 + ct + d

d²n/dt² = 10 − 6t
⇒ dn/dt = 10t - 3t² + c
⇒ n = 5t² − t³ + ct + d

Given n = 100 when t = 0. Sub above, get d = 100.

⇒ n = 5t² − t³ + ct + 100.

The given info enables us to eliminate one of the arbitrary constants only (d). The other one (c) cannot eliminate.