(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Differential operator method.

3. 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Use the differential operator to solve this differential equation

**Physics Forums | Science Articles, Homework Help, Discussion**