QUESTION $4$

$(4\mathrm{.}1)$ Using the method of undetermined coefficients, find a general solution of the differential equation

$2y^{\text{'}\text{'}}+4y^{\text{'}}=4x+10$

given that $y_1=1$ and $y_2=e^{-2x}$ are solutions of the corresponding homogeneous equation.

$(4\mathrm{.}2)$ Using the method of variation of parameters, find a general solution of the differential equation

$2y^{\text{'}\text{'}}+4y^{\text{'}}=4x+10$

given that $y_1=1$ and $y_2=e^{-2x}$ are solutions of the corresponding homogeneous equation.

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