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Question

Verify y=aex is a solution of d2ydx2y=0, find particular solution when y(0)=1.

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Solution

We have,

y=aex …… (1)


Differentiation this equation with respect to x and we get,

dydx=aex


Again, differentiation this equation with respect to x and we get,

d2ydx2=aex …… (2)


By equation (1) and (2) to, we get,

d2ydx2=y

d2ydx2y=0


Hence proved.


Now, put x=0 in equation (1) and we get,

y(0)=ae0

y(0)=a


Given that, y(0)=1

Then, a=1


Hence, this is the answer.


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