GATE (TF) Textile 2013 Question Paper Solution | GATE/2013/TF/33

Question 33 (Textile Engineering & Fibre Science)

The particular integral of $\frac{d^2y}{dx^2}+5\frac{dy}{dx}+6y=e^{2x}$ is

(A)	$\frac{e^{2x}}{20}$
(B)	$\frac{e^{2x}}{12}$
(C)	$2e^{2x}$
(D)	$4e^{2x}$

Answer / Solution

$\frac{d^2y}{dx^2}+5\frac{dy}{dx}+6y=e^{2x}$
or
$(D^2+5D+6)y=0$
$(m^2+5m+6)=0$
$(m^2+2m+3m+6)=0$
$(m+2)(m+3)=0$
m=-2 ,-3
Perticular integral(P.I.)= $\frac{1}{D^2+5D+6}\times e^{2x}$
P.I.= $\frac{1}{2^2+5\times 2+6}\times e^{2x}$
P.I.= $\frac{1}{20}\times e^{2x}$ (Ans)
Option A is correct

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