Find linearly independent functions that are annihilated by the given differential operator. (give as many functions as possible. use x as the independent variable. enter your answers as a comma-separated list.) d2 − 12d − 45

We want to find all such that

We have

so that either

or

These solutions are linearly independent; we confirm this by computing the Wronskian:

We can also confirm that these solutions are correct by substituting the solutions for in the differential equation:

a; x = 0.5

step-by-step explanation:

-10x = -5

x = 0.5

the solution, from the graphing of the two lines, is (3,2), i.e., x = 3, y = 2.