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7 marksDifferential Equations and Modeling

CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2 · Question 6(c)(i)

Show that the general solution to the differential equation 3(x^2 + x) dy/dx = 2y(1 + 2x) is y = C * ((x^2 + x)^2)^(1/3), where C in R.

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Other parts of this question

  1. 6(a)(i)Calculate the number of outcomes in the sample space.[3 marks]
  2. 6(a)(ii)Find the probability of obtaining exactly one head.[2 marks]
  3. 6(a)(iii)Calculate the probability of obtaining at least one head on the coins and an even number on the die on a particular attempt.[4 marks]
  4. 6(b)Determine whether y = C_1 x + C_2 x^2 is a solution to the differential equation (x^2 / 2) y'' - x y' + y = 0, where C_1 and C_2 are constants.[6 marks]
  5. 6(c)(ii)Hence, given that y(1) = 1, solve 3(x^2 + x) dy/dx = 2y(1 + 2x).[3 marks]

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