Consider the differential equation y '' − 2y ' + 37y = 0; ex cos(6x), ex sin(6x), (−[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 sincea) W(ex cos 6x, ex sin 6x) =

The question  is:

Consider the differential equation y'' - 2y' + 37y = 0;

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

a)

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

Because the Wronskian is not zero, we say the solutions are linearly independent