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Which of the following differential equ...

Which of the following differential equations has `y=c_1e^x+c_2e^(-x)`as the general solution?(A) `(d^2y)/(dx^2)+y=0` (B) `(d^2y)/(dx^2)-y=0` (C) `(d^2y)/(dx^2)+1=0` (D) `(d^2y)/(dx^2)-1=0`

Text Solution

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`y=c_1e^x+c_2e^(-x)`
differentiate with respect to x
`y'=c_1e^x-c_2e^(-x)`
differentiate with respect to x
`y''=c_1e^x+c_2e^(-x)`
`y''=y`
`y''-y=0`
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