(1) Find the general solution of the following differential equations. Use the method of undetermined coefficients to find a particular solution in each case. (a) y'' + y' + 4y = 2 sinh x (b) y'' - 2y' - 3y = 3xe^{2x}; y(0) = 1, y'(0) = 0 (2) Determine a suitable form for the particular solution y_p(x) if the method of undetermined coefficients is to be used. (DO NOT SOLVE THE EQUATION) (a) y'' + 2y' + 2y = 3e^{-x} + 2e^{-x} cos x + 4e^{-x}x^2 sin x (b) y'' + 3y' = 2x^4 + x^2e^{-3x} + sin 3x (3) Using the method of undetermined coefficients find the general solution of the following differential equation. y''' - y'' - y' + y = 2e^{-x} + 3 (4) Determine a suitable form for y_p(x) if the method of undetermined coefficients is to be used in the following differential equation. DO NOT EVALUATE THE CONSTANTS y^{(4)} + 2y''' + 2y'' = 3e^x + 2xe^{-x} + e^{-x} sin x
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Solving this equation gives the roots r = -1/2 ± √15i/2. Show more…
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