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`

Explanation

Correct option is B)


``
`frac{d y}{d x}=c_{1} e^{x}-c_{2} e^{-x}`


`frac{d^{2} y}{d x^{2}}=c_{1} e^{x}-c_{2} e^{-x}=y`


`frac{d^{2} y}{d x^{2}}-y=0`
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