GATE (TF) Textile 2010 Question Paper Solution | GATE/2010/TF/45

Question 45 (Textile Engineering & Fibre Science)

Solution of the differential equation \frac{d^2x}{dt^2}+6\frac{dx}{dt}+9x=0 will be

(A)x=(c_1+c_2t)e^{3t}
(B)x=(c_1+c_2t)e^{-3t}
(C)x=c_1e^{3t}+c_2e^{-3t}
(D)x=c_1e^{2t}+c_2e^{-3t}
[Show Answer]

\frac{d^2x}{dt^2}+6\frac{dx}{dt}+9x=0

We can write it as-

(D^2+6D+9)=0

(D^2+3D+3D+9)=0

(D+3)(D+3)=0

D=-3 .-3

X=c_1 e^{-3t}+tc_2 e^{-3t}

X=(c_1+tc_2)e^{-3t}

Option B is correct

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