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5 marksDifferential Equations and Modeling

CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2 · Question 2(b)(i)

Find the values of the constants m and n, given that y = m \cos x + n \sin x satisfies the differential equation \frac{\mathrm{d}^2y}{\mathrm{d}x^2} - 4\frac{\mathrm{d}y}{\mathrm{d}x} + 3y = 10 \sin x.

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Other parts of this question

  1. 2(a)(i)Find \int \frac{1}{x} \ln x \, \mathrm{d}x.[3 marks]
  2. 2(a)(ii)Solve the differential equation x^2 \frac{\mathrm{d}y}{\mathrm{d}x} + xy = \ln x.[5 marks]
  3. 2(b)(ii)Hence, find the general solution of the differential equation.[3 marks]
  4. 2(c)(i)Express \frac{2 + 3x - x^2}{(x - 1)(x^2 + 1)} in partial fractions.[6 marks]
  5. 2(c)(ii)Hence, find \int \frac{2 + 3x - x^2}{(x - 1)(x^2 + 1)} \, \mathrm{d}x.[3 marks]

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