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Which of the following differential equa...

Which of the following differential equations has `y=c_(1)e^(x)+c_(2)e^(-x)` as the general solution ?

A

`(d^(2)y)/(dx^(2))+y=0`

B

`(d^(2)y)/(dx^(2))-y=0`

C

`(d^(2)y)/(dx^(2))+1=0`

D

`(d^(2)y)/(dx^(2))-1=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Given general solution `y=c_(1)e^(x)+c_(2)e^(-x)`…………`(1)`
Differntiate w.r.t.x, `y'=C_(1)e^(x)+c_(2)e^(-x)(-1)`
Again differentiate w.r.t.x, `y''=c_(1)e^(x)-c_(2)e^(-x)(-1)`
`implies y''=c_(1)e^(x)+c_(2)e^(-x)`
`implies y''=y` [from equation `(1)`]
`implies y''-y=0`
which is the required differential equation of the given general solution.
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