OK, but I think the solution can be greatly simplified. First let sin 2x = 2 sin x cos x and sin³ ⁼ sin x (1 - cos² x), turning the generalized solution to: C₁ sin x + C₂ cos x - (x cos x)/2 + (sin x cos² x)/2 + sin x/2 - (sin x cos² x)/2 Note the (sin x cos² x)/2 terms nicely cancel each other out, while the two sin x terms can be combined with a new constant. So the solution reduces to: C₁ sin x + C₂ cos x - (x cos x)/2 To check this result, you can determine that y = -(x cos x)/2 is a particular solution to the differential equation.
@leahgrace5463
3 жыл бұрын
thanks! i was struggling on the simplification
@maxpercer7119
2 жыл бұрын
nice, using the method of undetermined coefficients , y = y_c + y_p, one obtains a much more efficient solution. clearly he is trying to show the method of variation of parameters which produces an ugly result, but solves more differential equations
@infinitasalo472
4 жыл бұрын
Essentially, I learned Variation of Parameters entirely from this video (during quarantine). Thank you
@TheMathSorcerer
4 жыл бұрын
Excellent!
@aldrchase
4 жыл бұрын
"I'm gonna put this in a box because it's an accomplishment" Whenever I finally solve for a difficult building block I always have an insatiable urge to box it :)
@TheMathSorcerer
4 жыл бұрын
Haha yes!
@shannonholcroft3311
5 жыл бұрын
I was trying to solve this same problem using undetermined coefficients and somehow got stuck. This really helped! Thanks.
@TheMathSorcerer
5 жыл бұрын
Awesome!
@jumpoutatree
Жыл бұрын
I followed how you obtained W2 using u-sub, but I used the following identity 2cosxsinx = sin2x , therefore cosxsinx = (sin2x/2), which I integrated to -(cos2x)/4. Completely different answer. Is that identity correct? I got it from the wikipedia entry on trig identities.
@kimutaivictor7011
5 жыл бұрын
Very helpful. Thanks so much for sharing your experience.
@meatballcarmnasalhose3301
5 жыл бұрын
Lot of help
@rivers3408
6 ай бұрын
I was confused because the back of the book had a different answer but im glad I watched until the end. I got what you got and you said that its different from the answer in the back because you didnt apply the identities. Thank you again! I told my friend to check out your channel because he likes collecting math books
@iwilld0it
2 жыл бұрын
Nice! The extended exponential response formula is another good technique for this particular problem.
@RuffHooptie
5 жыл бұрын
This guy is a God.
@AndrewColwell-g5h
11 ай бұрын
I was loosing my mind thinking I got the answer wrong. Thank you so much for this video!!
@TheRadems
4 жыл бұрын
not a huge fan of math but if you were my teacher i would love math
@TheMathSorcerer
4 жыл бұрын
thanks man
@duncancrogan9943
3 жыл бұрын
Thanks for the tutorial, very detailed and I like your style as well!
@TheMathSorcerer
3 жыл бұрын
Thank you👍
@austinculp3169
4 жыл бұрын
been stuck on this problem for a while. Thanks!
@Rohit.yadav-860
2 жыл бұрын
Thank you so much sir
@kandhadally96
3 жыл бұрын
It was very helpful .. But sir I had one doubt because one question has I'm not solved... could you tell me please... Solve (y cos x+sin y+y)dx+(sin x+x cos y+x)dy=0
@ANDRES7SANDOVAL
4 жыл бұрын
Yo quiero que sea mi profesor de universidad. Saludos desde Mexico!
@TheMathSorcerer
4 жыл бұрын
Saludos!
@mishthiexplores3732
3 жыл бұрын
hey Newton ! are you there??? really? its really great experience to learn something in maths by someone very close to newton both in appearance and knowlede
@TheMathSorcerer
3 жыл бұрын
Haha
@beeneeweenee
4 жыл бұрын
Very wise tutorial, Arithmetic Archmage.
@TheMathSorcerer
4 жыл бұрын
Thank you!!
@leandrobalmaceda5631
5 жыл бұрын
Thank you!
@TheMathSorcerer
5 жыл бұрын
😄
@RachelWard1137
2 жыл бұрын
"omg my answer's different" yep
@Maxi-ff6to
Жыл бұрын
I really miss such teachers in university.
@Chukaye1
4 жыл бұрын
How WOULD you simplify this?
@Jjdniss
4 жыл бұрын
same question haha, it seems yp ends up as (-xcos(x))/2
@UrduQuiz786
2 жыл бұрын
Sir thanks
@chamelimajumder6296
3 жыл бұрын
Thnx a lot❤️❤️
@blahmadgaming8531
3 жыл бұрын
Sir my sir has given me this same question but with undetermined coefficient???what do i do?
@mirkopoliti310
5 жыл бұрын
why alpha and beta, are respectively 0 and 1 ?
@choukriazzouzi5796
4 жыл бұрын
Cuz the solution of m²=-1 So m = alpha +i*beta And m=-i or m=i Alpha = 0
@TheMathSorcerer
4 жыл бұрын
Yup!
@connorplatt3761
4 жыл бұрын
thank you, I was so close
@TheMathSorcerer
4 жыл бұрын
You are welcome👍
@minhang8429
4 жыл бұрын
y" + y = x.cos(x) someone help me :(
@karamrahaf4469
3 жыл бұрын
Thanks, y'' = y sin(x)
@karamrahaf4469
3 жыл бұрын
solved
@حذيفهضمور
4 жыл бұрын
y"+4y=3cos2x please solve if you have time
@SoniaJbrt
Жыл бұрын
This is as confusing to me as it was in High School. No idea.
@venketswararaopadala437
3 жыл бұрын
(Variation of parameters )solve (dsquare+1)y=4xsinx
@zonezee
4 жыл бұрын
what if the equation will be y"+y=5sint?
@TheMathSorcerer
4 жыл бұрын
very similar you just have a 5 there.
@zonezee
4 жыл бұрын
@@TheMathSorcerer so it mean the variation of parameters can also be use to get the exact answer even though we will not use the undetermined coeffients?
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