question_answer

The general solution of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}+y=2{{e}^{3x}}\] is given by

A)  \[y=({{c}_{1}}+{{c}_{2}}x)\,\,{{e}^{x}}+\frac{{{e}^{3x}}}{8}\]

B)  \[y=({{c}_{1}}+{{c}_{2}}x)\,\,{{e}^{-x}}+\frac{{{e}^{-3x}}}{8}\]

C)  \[y=({{c}_{1}}+{{c}_{2}}x)\,\,{{e}^{-x}}+\frac{{{e}^{3x}}}{8}\]

D)  \[y=({{c}_{1}}+{{c}_{2}}x)\,\,{{e}^{x}}+\frac{{{e}^{-3x}}}{8}\]

E)  None of these