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3 marksDifferential Equations and Modeling

CAPE Pure Mathematics Unit 2 · May/June 2021 · Paper 2 · Question 6(a)(ii)

A differential equation is given as dy/dx = tan x + y - 2 cos² x = 0.

Hence, determine the particular solution given that y(π/2) = 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 = 5/3 + 1/3 cos 2x + C cosec x, where C is a constant.[10 marks]
  2. 6(b)(i)Determine the general solution of the differential equation y'' + 2y' + 5y = 0.[7 marks]
  3. 6(b)(ii)Hence, determine the solution of the boundary value problem y'' + 2y' + 5y = 0 with y(0) = 1, y'(π) = 2.[5 marks]

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