CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2 · Question 6(a)(ii)
Hence, given that y = 2 when x = 0, calculate y(1).
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- 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}.[7 marks] - 6(b)(i)Use the substitution
u = y'to show that the differential equationy'' + 4y' = 2\cos 3x - 4\sin 3xcan be reduced tou' + 4u = 2\cos 3x - 4\sin 3x.[2 marks] - 6(b)(ii)Hence, or otherwise, find the general solution of the differential equation.[13 marks]
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