Consider the differential equation y'' − y' − 30y = 0. Verify that the functions e−5x and e6x form a fundamental set of solutions of the differential equation on the interval (−[infinity], [infinity]). The functions satisfy the differential equation and are linearly independent since the Wronskian W (e−5x, e6x) = ?

Step-by-step explanation:

We have to take the derivatives for both functions and replace in the differential equation. Hence

for y=e^{-5x}:

for y=e^{6x}:

Now we replace in the differential equation  y'' − y' − 30y = 0

for y=e^{-5x}:

for y=e^{6x}:

Now, to know if both function are linearly independent we calculate the Wronskian

I hope this is useful for you

Best regard

i think the answer is b.

step-by-step explanation:

not 100% sure though.

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step-by-step explanation:

because that's the answer