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Question

The general solution of the differential equation d2ydx2+8dydx+16y=0 is


A

(A+Bx)e5x

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B

(A+Bx)e-4x

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C

(A+Bx2)e4x

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D

(A+Bx4)e4x

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Solution

The correct option is B

(A+Bx)e-4x


Find the general solution of the differential equation

Given, d2ydx2+8dydx+16y=0

Put D=ddx

(D2+8D+16)y=0D2+8D+16=0D2+4D+4D+16=0D(D+4)+4(D+4)=0(D+4)(D+4)=0D=-4,-4

Since, roots are real and equal.

General Solution is y=(A+Bx)e-4x

Hence, option (B) is the correct answer.


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