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5 marksDifferential Equations and Modeling

CAPE Pure Mathematics Unit 2 · May/June 2019 · Paper 2 · Question 6(a)(i)

A differential equation is given as x(dy/dx) + y = 2 sin x.

Show that the general solution of the differential equation is y = (c/x) - (2/x) cos x, where c is a constant.

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Other parts of this question

  1. 6(a)(ii)Hence, determine the particular solution of the differential equation that satisfies the condition y = 2 when x = π.[3 marks]
  2. 6(b)Show that the general solution of the differential equation dy/dx = (xy - y) / (x² - 4) is y = k(x - 2)^(1/4)(x + 2)^(3/4), where k is a constant.[7 marks]
  3. 6(c)Solve the boundary-value problem y'' - y' - 2y = 0, given that when x = -1, y = 1 and when x = 1, y = 0.[10 marks]

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