Consider the differential equation: y '' − 2y ' + 17y = 0; e^x cos 4x, ex sin 4x, (−[infinity], [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(e^x cos 4x, e^x sin 4x) = ≠ 0 for −[infinity] < x < [infinity]. Form the general solution. y =

The question is:

Consider the differential equation:

(1) Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since

(2) Form the general solution.

(1) To verify if the given functions form a fundamental set of solutions to the differential equation, we find the Wronskian of the two functions.

The Wronskian of functions is given as

(2) The general solution may be expressed as a linear combination

Where are arbitrary constants.