Engineering Mathematics $($I$)$ Homework $6-5$

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In terms of the annihilator approach, solve the given differential equation by undetermined coefficients as follows.

$($a$)y^{\text{'}\text{'}}{y}^{\text{'}}\frac{1}{4}y=e^x(sin3x-cos3x)$

$($b$)y^{(4)}-4y^{\text{'}\text{'}}=5x^2-2e^{2x}$

$($c$)y^{\text{'}\text{'}\text{'}}-y^{\text{'}\text{'}}{y}^{\text{'}}-y=x{e}^x-e^{-x}7$