Question 5 (20 Marks) Using Method of Undetermined, solve the following differential equation. $4y'' + 8y' = 3 \cos x + 6 \sin x$
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The characteristic equation is 4r^2 + 8r = 0. Factoring out 4r, we get 4r(r + 2) = 0. So the roots are r = 0 and r = -2. Therefore, the complementary solution is y_c = C1e^(0x) + C2e^(-2x). Simplifying, we get y_c = C1 + C2e^(-2x). Show more…
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Question 6 (20 marks) (i) By solving its auxiliary equation, find the complementary function of the Differential Equation d^2y/dx^2 - 3 dy/dx + 2y = 0. (ii) Find the particular integral for the differential equation d^2y/dx^2 - 3 dy/dx + 2y = 4x - 5. (iii) Using your answers to (i) and (ii), write down the general solution to the Equation d^2y/dx^2 - 3 dy/dx + 2y = 4x - 5. and hence find the solution which satisfies the initial conditions y(0) = 1, y'(0) = -1.
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