Verify that the function `y=e^(-3x)` is a solution of the differential equation `(d^2y)/(dx^2)+(dy)/(dx)-6y=0`

Explanation

`y=e^{-3 x}`


Differentiating equation with x, we find


`frac{d y}{d x}=-3 e^{-3 x}`


Differentiating equation again with x, we find


`frac{d^{2} y}{d x^{2}}=9 e^{-3 x}`


Now put the value in `frac{d^{2} y}{d x^{2}}+frac{d y}{d x}-6 y`


`=9 e^{-3 x}-3 e^{-3 x}-6 e^{-3 x} `


`=0`


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