Question

0. The Particular integral of the differential equation( D2+D+1)y=ex is equual to
(A) 1/3.ex
(B) 3ex
(C) ex
(D) none of these​

Answer 1

$\textbf{Given:}$

$\textsf{Differential equation is}$

$\mathsf{(D^2+D+1)y=e^x}$

$\textbf{To find:}$

$\textsf{Particular integral of the given differntial equation}$

$\textbf{Solution:}$

$\underline{\textsf{Particular integral}}$

$\mathsf{=\dfrac{e^x}{D^2+D+1}}$

$\boxed{\mathsf{Paricular\;integral\;of\;\dfrac{e^{ax}}{f(D)}\;is\;\dfrac{e^{ax}}{f(a)}\;provided\;f(a)\neq\,0}}$

$\mathsf{=\dfrac{e^x}{1^2+1+1}}$

$\mathsf{=\dfrac{e^x}{1+1+1}}$

$\mathsf{=\dfrac{e^x}{3}}$

$\implies\boxed{\mathsf{Particular\;integral=\dfrac{e^x}{3}}}$

$\textbf{Answer:}$

$\mathsf{Option\;(A)\;is\;correct}$

$\textbf{Find more:}$

Find the Particular Integral of y" + 2y' + 3y = Sin x is

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