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1. Determine the form of a particular solution for the following differential equations. (Do not evaluate...

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Advance Math

1. Determine the form of a particular solution for the followingdifferential equations. (Do not evaluate the coefficients.)

(a) y'' − y' − 6y = x^2 e^x sin x + (2x^3 − 1)e ^ cos x.

(b) y'' − y' − 6y = (2 − 3x^3 )e^3x .

(c) y'' + 4y' + 4y = x(e^x + e^−x )^2 .

(d) y'' − 2y' + 2y = (x − 1)e^x sin x + x^2 e^−x cos x.

2. Find a general solution to the differential equation y'' −3y' + 2y = x^2 + 1 − x sin x + xe^2x

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