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7 marksDifferential Equations and Modeling

CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2 · Question 6(a)(i)

Find the general solution of the differential equation (1 + x^2) \frac{\mathrm{d}y}{\mathrm{d}x} + 2xy = \sqrt[3]{x}.

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Other parts of this question

  1. 6(a)(ii)Hence, given that y = 2 when x = 0, calculate y(1).[3 marks]
  2. 6(b)(i)Use the substitution u = y' to show that the differential equation y'' + 4y' = 2\cos 3x - 4\sin 3x can be reduced to u' + 4u = 2\cos 3x - 4\sin 3x.[2 marks]
  3. 6(b)(ii)Hence, or otherwise, find the general solution of the differential equation.[13 marks]

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