Determine the form of a particular solution, second order linear differential equation, sect 4.4 #27

Determine the form of a particular solution,
Form of a particular solution with undetermined coefficients,
particular solution for a non-homogeneous differential equation,
second order non-homogeneous linear differential equations,

For more calculus and differential equations tutorials, check out my new channel "just calculus":

To learn how to solve different types of differential equations:

#DifferentialEquations

[allybarajas]

Taught me more in 5 minutes than my professor did in over an hour. Thank you.

[amadfriends]

so, you'll look at Yh, and you'll look at Yp, if one part of Yh has the same power or the same equation in Yp, you'll multiply it with another t and you will look again and again and multiply by t until you don't have a duplication.

[disagree]

Sir, you just saved me with this video. Thank you so much for explaining this in such a clear, concise way.

[luiskruger]

what happens if a constant is added to the right hand of the equation? so instead of 4t^3(sin(3t)), its just sin(3t) + 9 or something?

[antiquarian]

Doesn’t the t^3 multiplied by the sin and cos make it different from the homogeneous solution?

[sebyinho]

I love how I can see that you enjoy doing this, I begin Differential Equations next semester and your enthusiasm is like an inspiration to me!

[jrt]

If I encounter this on competitive exam, and I have to prove it, should I use this guessing method or variation of parameter?

[thisismycoolnickname]

I made a guess that the particular solution would be (u sin3t + v cos3t), put it into the equation and solved for u and v.
I got u = 1/3 t^3 - 1/54 t and v = -1/6 t^4 + 1/18 t^2

[Tom-lgmu]

does this work the same if the sin was replaced with cos?

[AN-bwim]

Why can you multiply by t? I don't understand that part.

[dingwahliaw]

Should be (Yp") and solve A to H👀??

[spartakharutyunyan]

dude i got 94 just watching your videos! good job!!

[sepm]

do you have any video using the key identity evaluation method? im having a hard time finding videos or examples using that method instead of the undetermined coefficient

[sivemahlatini]

I'm still confused if why did you multiply by t... i like ur videos alot

[msduff]

Dude you saved me again! You're the best!

[elijah]

ignore my troll like name but these videos are extremely helpful and very well done. This should help me pass my exam tomorrow

[rhiannaullom]

Omg you’re so cute! 😍 Haha but this genuinely helped me a lot, thanks for sharing this!

[DougCube]

It doesn't look good when you write the '=' directly below the square symbol like that at 3:06.

[abhishanand]

i cried after the end of this video cause i finally got it

[meliodas-sama]

He used a blue pen, which means that this topic is that hard.