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Suppose f(x)=e^(a x)+e^(b x) , where a!=...

Suppose `f(x)=e^(a x)+e^(b x)` , where `a!=b ,` and that `f^(x)-2f^(prime)(x)-15f(x)=0` for all `xdot` Then the value of `(|a b|)/3` is ___

A

25

B

9

C

-15

D

-9

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \(|ab|/3\) given the function \(f(x) = e^{ax} + e^{bx}\) and the differential equation \(f''(x) - 2f'(x) - 15f(x) = 0\). ### Step-by-Step Solution: 1. **Define the function and its derivatives:** \[ f(x) = e^{ax} + e^{bx} \] ...
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