The general solution of the differential equation y'' + 2y' + 5y = 4\sin 2t is y = CF + PI, where CF is the complementary function and PI is a particular integral. Calculate the roots of \lambda^2 + 2\lambda + 5 = 0, the auxiliary equation.
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Practise this question\cos x \frac{dy}{dx} + y\sin x = 2x\cos^2 x.[7 marks]y = \frac{15\sqrt{2}\pi^2}{32} when x = \frac{\pi}{4}, determine the constant of the integration.[5 marks]CF), the general solution of y'' + 2y' + 5y = 0.[3 marks]PI) is u_p(t) = A\cos 2t + B\sin 2t, show that A = -\frac{16}{17} and B = \frac{4}{17}.[3 marks]y(0) = 0.04 and y'(0) = 0, obtain the general solution of the differential equation.[5 marks]More practice: the rest of this paper · more Differential Equations and Modeling questions · all CAPE Pure Mathematics Unit 2 past papers