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## Homework Statement

Use the differential operator method to find a fundamental set of solutions {y_1(x), y_2(x)} of the equation

d^2 y/dx^2 - 18 dy/dx + 90y = 0.

## Homework Equations

Differential operator method.

## The Attempt at a Solution

I have a huge problem understanding how to use the differential operator method. I can successfully complete this problem using the characteristic equation:

r^2 - 18r + 90 = 0

r = 9 +/- 3i

y_1(x) = e^(9x) * cos(3x)

y_2(x) = e^(9x) * sin(3x)

but I really need to understand how to use the differential operator and I don't get anything I read on the internet or in my text book.

A comparison (with contrasting) to the method with the characteristic equation would be GREATLY appreciated!

Thanks in advance!

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