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7 marksDifferential Equations and Modeling

CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 2 · Question 6(b)(ii)b)

A differential equation is given as y'' - 2y = 0.

Hence, show that the solution which satisfies the boundary conditions y(0) = 1 and y'\left(\frac{\sqrt{2}}{2}\right) = 0 is y = \frac{1}{e^2 + 1}\left(e^{\sqrt{2}x} + e^{2 - \sqrt{2}x}\right).

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Other parts of this question

  1. 6(a)(i)Construct a tree diagram to show the probabilities that Alicia arrives at school.[3 marks]
  2. 6(a)(ii)What is the probability that Alicia is at school on any given school day?[3 marks]
  3. 6(a)(iii)Given that Alicia is at school today, determine the probability that it is a rainy day.[4 marks]
  4. 6(b)(i)Show that the equation y + xy + x^2 = 0 is a solution of the differential equation \frac{dy}{dx} = \frac{y - x^2}{x(1 + x)}.[5 marks]
  5. 6(b)(ii)a)Find the general solution of the differential equation.[3 marks]

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