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4 marksDifferential Equations and Modeling

CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 2 · Question 6(b)(i)

A differential equation is given as y'' + 2y' + y = x e^(-x).

Determine the solution of the complementary equation y'' + 2y' + y = 0.

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Other parts of this question

  1. 6(a)(i)Show that the general solution of the differential equation is y = (1/2) sec(x) - cos(x) + C sec(x).[9 marks]
  2. 6(a)(ii)Hence, or otherwise, solve the initial value problem y' cos(x) = y sin(x) + sin(2x), y(0) = 0.[2 marks]
  3. 6(b)(ii)Given that the particular solution has the form y_p = (A x^3 + B x^2) e^(-x), or otherwise, determine the general solution of the differential equation.[10 marks]

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