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

Suppose `f(x)=e^(ax) + e^(bx)`, where `a!=b`, and that `fprimeprime(x)-2fprime(x)-15f(x)=0` for all `x`. Then the value of `ab` is equal to:

A

25

B

9

C

-15

D

-9

Text Solution

AI Generated Solution

To solve the problem, we start with the function given: \[ f(x) = e^{ax} + e^{bx} \] where \( a \neq b \). We are also given the differential equation: \[ f''(x) - 2f'(x) - 15f(x) = 0 \] ...

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