A Level H2 Math - Differential Eqns

• Jasmine ngjiamin

  19 Dec 13, 11:16

  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

• Mad Hat

  19 Dec 13, 16:37

  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.