undetermined coefficients, example 4 (KristaKingMath)

In this video we'll learn how to use the method of undetermined coefficients to find the particular solution to the second-order nonhomogeneous differential equation. In order to do this, we'll have to first find the complementary solution. Then we'll make a guess about the particular solution, take its first and second derivatives, and then plug those back into the original differential equation in order to solve for the coefficients in the particular solution. The sum of complementary and particular solutions will be the general solution of the differential equation.

● ● ● GET EXTRA HELP ● ● ●

● ● ● CONNECT WITH KRISTA ● ● ●

Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[full-metal_jacob]

Been trying to figure out the multiplicity part for about 5 hours now.
You explained it in 2 minutes. Thank you!!!

[zianiera]

You have given us the best explanation in the whole world.Thank you

[riceCAD]

your voice is so lovely :) thank you for posting this!

[_sidxd]

Omg Tysm this was the best video on youtube for clearing out the yp part!

[daleadrianlongno]

Thanks so much Krista!! You've basically helped me in all of differential and integral calculus up until now in differential equations!! Such a generous god :)

[HeyitsCalifornia]

Just curious what program do you use to make your videos? I especially like the chalkboard effect in your older videos.

[sal_tal]

thank you very much i have been looking for an example like this all day, u might never see my comment because this video is 5 years old but still I'm greatful to you.

[mea]

Best explanation for the particular solution. Thank you!

[bachnguyenxuan]

You're the best teacher, so i hope you have motivation in your life
Thank you very much

[kevinkundu]

wow!!! you're the Best clear and direct presentation...I love it !!!...

[adarshkumarjha]

Ummm tell me
Do we only have to multiply x to the terms which are repeated or we gotta multiply x to each term of particular solution

[sumangupta]

This kind of equations were nightmare for me but thanks to you I managed to grab it.. A big thanks

[mateogonzalez]

Like 30 mins looking for an example of right side multiplication and finally found one, ty Lord. And thanks to you :D

[humayra]

Can you please solve this problem? I'm struggling to understand it.
1)y"+y=3sin(2t)+ t cos(2t)
, What is yp(particular equation) here? And how we find it?

[winstrengh]

Very interesting, thank you I had so much fun with your video thank you sooo much ❤

[erikmjelde]

super helpful especially the method you used to keep all this organized

[Yasiir_alii]

I do not know how thank you
Many thanks 👏🏻👏🏻

[yuhoseok]

This makes super clear. Awesome video to review. Thanks a lot!!

[blahhhh]

do we just have to multiply x with the term in Yp similar to Yc or with the whole Yp?

[VroniWolf]

wow what a great step by step explanation! thank you soo much! :)