Use the method of undetermined coefficients to find one solution of

y'' + 4y' - y = 3exp(1t)

y = ?
(It doesn't matter which specific solutoin you find for this problem)

Question

Use the method of undetermined coefficients to find one solution of

y'' + 4y' - y = 3exp(1t)

y = ?
(It doesn't matter which specific solutoin you find for this problem)

apples · Answer

A good guess will be y=Ae^{t} for some A. Plugging in, you get:$$Ae^t + 4Ae^t - Ae^t = 3e^t$$which reduces to $$4Ae^t = 3e^t$$ thus A = 3/4.

Therefore a particular solution is $$Y_p = \frac{3}{4}e^t$$

anonymous · Answer

Thank you. I thought we had to solve the homogeneous equation first using auxiliary equations. That's where I got confused.

apples · Answer

A note: You do sometimes need the complementary solution when using the method of undetermined coefficients if you run into problems with your guess.

anonymous · Answer

Yeah, I know that. I should have just been a Biology major to begin with instead of Electrical Engineering and Physics. Math above Calculus III have beome my weakness. Now, I'm trying to figure out the next problem. Thanks for your help though. I appreciate it.

apples · Answer

No problem!