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Question

The differential equation d2ydx2+6dydx+9y=6e3x has boundary conditions y(0)=0,y(+1)=6e3

then y(1) is

  1. 0

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Solution

The correct option is A 0

Given ,

[D2+6D+9]y=6e3x

So, auxiliary equation is,

m2+6m+9=0

(m+3)2=0

m=3,3

So, complimentary function, C.F is [C1+C2x]e3x ... (i)

Now, P.I=1D2+6D+96e3x

For D = -3 case fails so ,

P.I=6xe3x2D+6

Again for D = -3 case fails so,

P.I=6x2e3x2=3x2e3x ... (ii)

Using (1) and (2)

So, complete solution is ,

y=[C1+C2x]e3x+3x2e3x

y=[C1+C2x+3x2]e3x

Now, y(0)=0

0=[C1]e3.0

C1=0

Also, y(1)=6e3

[C2+3]e3=6e3

C2=3

So, y=[3x+3x2]e3x

y(1)=[3+3]e3=0


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