Second-Order Non-Homogeneous Differential (KristaKingMath)

Second-Order Non-Homogeneous Differential Equations calculus problem example.

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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?!”

[kristakingmath]

I always hated when the details were skipped over, so I do my best not to. :)

[djm]

these vids from almost a decade ago are still the absolute best

[sanlistonmadzima]

Thank you so much. I'm a particular fan of how you show every single step, even the arithmetic. I really appreciate that. I am subscribing.

[bronwynlaird]

you even reply to everybody's questions. wow you are truely amazing.

[edukate_eng]

So so so helpful! Very well explained. Especially the bit about the particular solution and multiplying by x to get rid of overlapping. Thank you!

[kristakingmath]

If you subtract that portion, then it just moves from the right hand side to the left hand side, and you're still looking at a nonhomogeneous DE. Homogenous means you've got only y's on the left, that are set equal to 0 on the right.

omg thank you so much for this, please continue making videos, you have no idea how much people you are helping through this, I even told some of my classmates about your channel, keep up the great work!! 

[kristakingmath]

it would change it, but that's exactly what you want to do. remember that, at that step, you're trying to figure out what the particular solution IS, and you haven't settled on the answer yet. so you're not changing something that's already correct, you're trying to figure out what the correct solution is. multiplying by x is something you have to do to get to the correct particular solution. hope that helps clarify things... :)

[brandoncastaneda]

This channel has been the biggest help in all of my college math courses for the past couple years. You're the best!

[kevinlafuente]

hi Krista! i just used, to get particular solution to the same problem above, these methods:
1. solving y(x) by replacing C1 and C2 with U1 and U2 respectively. It will turn out like this y(x)= u(1) + u(2)e^(-2x). Then determine the unknown u's by getting the 1st and 2nd derivative of the new y(x), then solve them simultaneously. (I have watch it using to solve 2nd orders from different video)
2. solving yp(x)= -y(1)∫[y(2)*g(x)]/W(x, y) + y(2)∫[y(1)*g(x)]/W(x, y) (seen from your separate vid Variation of Parameters for DE)

and I got the same particular solution: 6x^2 -6x -xe^(-2x)/2 -e^(-2x)/4 +3
It have the last two more terms which are not in your solution. So, is this particular solution also valid? or it is definitely wrong?
and if it is, have I used the methods improperly? or the methods I mentioned are just not valid for the problem concern in the video?

P.S. I really like your videos. They're easy to understand and are reasons why I enjoyed solving DE now. Thank you for all the enlightenment. :)

[jandon]

I've watched your videos since calc 1 and you still help me to this day! Diff eq can be tricky but you make it so easy to understand!! Thank you for your contributions, the older students like myself appreciate all your dedication!

[lukasodern]

Finally someone who explains why you sometimes have to multiply the particular solution with x!
Thank you!

[kristakingmath]

Thank you so much, Michael! I really hope your students will find my videos helpful when it comes to mastering differential equations! :D

[ahmedmusa]

without you and professor Leonard channel 80% of students would never pass calculus exams
you are the real teachers

[kristakingmath]

@Romankidful You're welcome! Glad you found it easy to follow.

[ponyluvr]

Thank you so much for all you do on this channel! These are the best examples that I have seen online and there is more than one question so we can check if we actually know it. I have told all my friends about this channel and they all love it too. Thank you for all the time that you put into this! It is because of you that I have hope on my final. Please keep posting these amazing videos!

[theastronomiefreak]

Wow! Thank you so much! Ive been looking through youtube for hours not finding anything useful, until now :)

[ura]

That was a very good explanation, I always found this type of problem disturbing. .. thank you so much.

[ricardozuniga]

You are awesome! I have a test coming up and neither my book nor my professor had really helped me fully understand what to do in the case of duplication. Looks like there's a new Khan in town ;) Thanks Krista. Subscribed.

[crispyhaole]

Wow. Just Wow. 21 minutes to cover what my professor failed to in a 3 hour lecture. More detailed, more cases covered, and much more clear. I'm better off cutting class and watching you. You are an ANGEL!