Thread: Second order linear ODE

Just wondering how would you find the particular solution to the following differential equation. Is there a quick technique or way of doing this?

Inspired guesswork.

Note that the right hand side can be expanded as .


So an appropriate particular solution could be .

This means




and

.


Substituting into the DE gives...





.


Therefore and .

This gives

and



.


So finally, we have our particular solution

.