Consider the differential equation y'' − y' − 20y = 0. Verify that the functions e−4x and e5x 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−4x, e5x = ≠ 0 for −[infinity] < x < [infinity].Form the general solution. y =

Therefore and are fundamental solution of the given differential equation.

Therefore   and are linearly independent, since

The general solution of the differential equation is

Step-by-step explanation:

Given differential equation is

y''-y'-20y =0

Here P(x)= -1, Q(x)= -20 and R(x)=0

Let trial solution be

Then,   and  

Therefore the complementary function is =

Therefore and are fundamental solution of the given differential equation.

If and are the fundamental solution of differential equation, then

Then   and are linearly independent.

Therefore   and are linearly independent, since

Let the the particular solution of the differential equation is

and

Here , , ,and  

       =0

and

       =0

The the P.I = 0

The general solution of the differential equation is

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )

step-by-step explanation:

if you want to separate 54 into 6 individual tiers then you need to divide if you want to separate 54 into 6 individual tiers then you need to divide 6 and 54.

if you divide 9 by 6 you will get 54.

- hope i .