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There are 3 problems in the first part of this homework assignment. Consider the following second...

There are 3 problems in the first part of this homework assignment. Consider the following second order nonhomogeneous linear differential equations

(1) y ′′ + 100y = 36 cos(8x) + 72 sin(8x)

(2) y ′′ − 4y ′ + 3y = (2 − 12x)e x + (60 + 40x)e 3x

(3) y ′′ − 2αy ′ + α 2 y = 60xeαx + 60x 2 e αx ,

where α 6= 0 is a real nonozero constant. Use the method of undetermined coefficients to find a particular solution for each equation. Then solve each equation for real general solution.

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