Statistics Solutions

[See] (a) Verify that y_p_1=3 e^2 x and y_p_2=x^2+3 x are, respectively, particular solutions

Question: (a) Verify that \(y_{p_{1}}=3 e^{2 x}\) and \(y_{p_{2}}=x^{2}+3 x\) are, respectively, particular solutions of

\[\begin{aligned} y^{\prime \prime}-6 y^{\prime}+5 y &=-9 e^{2 x} \\ \text { and } \quad y^{\prime \prime}-6 y^{\prime}+5 y &=5 x^{2}+3 x-16 \end{aligned}\]

(b) Use part (a) to find particular solutions of

\[y^{\prime \prime}-6 y^{\prime}+5 y=5 x^{2}+3 x-16-9 e^{2 x}\]

and \(y^{\prime \prime}-6 y^{\prime}+5 y=-10 x^{2}-6 x+32+e^{2 x}\).

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