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Question

The solution of d3ydx38d2ydx2=0 satisfying y(0)=18, y1(0)=0 and y2(0)=1 is [here yn(x)=dnydxn]

A
y=18(e8x8x+78)
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B
y=18(e8x8+x+78)
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C
y=18(e8x8+x78)
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D
y=14(e8x8x+78)
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Solution

The correct option is A y=18(e8x8x+78)
Given, d3ydx38d2ydx2=0
y3(x)y2(x)=8
Integrating, we get,
lny2(x)=8x+C1
Putting x=0, we have C1=lny2(0)=ln1=0
lny2(x)=8x or y2(x)=e8x
y1(x)=e8x8+C2
Again, putting x=0, we have C2=18
So, y1(x)=18(e8x1)y=18(e8x8x)+C3
Putting x=0, we have C3=18164=764
Thus y=18(e8x8x+78)

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