SRL Archive - Mathematics

EDIT: Closed (None were able to be answered)

I'm currently finishing 2nd year Electrical engineering at U of T, and in need of some aid with a Math assignment.

I'm not sure if anyone on the SRL community is able to do this type of math, but seeing as many of you are so good at scripting, I'll give it a shot.

Here are the 5 questions (HINTS in my 2nd post below):

Well I go to GBC.. pretty sure u know what that is since ur a toronto student as well.. I've seen this math and can't do it (only a few I can get) but it's extremely hard man.. Iunno if anyone is going to take the time to do it.

Any hints? Cuz that's a lot of questions.

Here is what I've gotten. Its been a bit since I've done DiffEq so no guarantee they are correct :p Don't have time to bother with general solutions for #1, 2, 5. And you should at least do some yourself or you will never pass the final ;)

#3
y1 = t-sin(2t)+cos(2t)+1
y2 = 2t+6sin(2t)+cos(2t)-(1/2)

#4
y1 = -4e^(-3t)+16e^(2t)+e^(3t)-2
y2 = e^(-3t)(8e^(5t)+3)

From: Hobbit
Here is what I've gotten. Its been a bit since I've done DiffEq so no guarantee they are correct :p Don't have time to bother with general solutions for #1, 2, 5. And you should at least do some yourself or you will never pass the final ;)

#3
y1 = t-sin(2t)+cos(2t)+1
y2 = 2t+6sin(2t)+cos(2t)-(1/2)

#4
y1 = -4e^(-3t)+16e^(2t)+e^(3t)-2
y2 = e^(-3t)(8e^(5t)+3)

Ah, they didn't seem to be correct: got 2 tries left on both of them
(Thanks for the attempt lol)
And yeah, I tried some other questions myself (there are 8 in total), could only get 3

From: ggzz
Well I go to GBC.. pretty sure u know what that is since ur a toronto student as well.. I've seen this math and can't do it (only a few I can get) but it's extremely hard man.. Iunno if anyone is going to take the time to do it.

Any hints? Cuz that's a lot of questions.

Ah, nice to know there are some Toronto people on SRL, haven't seen Brown myself though.
I've uploaded hints corresponding to each question (hint 1 = question 1, etc.)

I am of no help, even though I should be. I have been through all of my diff eq classes but I never really kept up with them to be able to help, sorry :(

I was at toronto from elementary to high school, but am at ubc for uni. Definitely nice to see others too :P

differentiate the given y1 and fill in y1' and y1 in the first equation and solve for y2 to get y2 = c1e^-t + 66e^-2t, not sure if you can solve c1 aswell, I don't think so though

you can do the same for 2 to get y2 = c1e^4t - 5/2 c2 e^-3t - 10 (you can fill in the second equation to check if it's true)

Solve for #1
y2=c2*e^(-t)-33*e^(-2t)
___________
Homogenic part: y1h=c1*e^(t)-c2*e^(-t) y2h=c2*e^-t (used the eignvec, eignval method)
I used Ansatz for the inhomogenic part (y1ih=A*e^(alpha*t)+B*e^(betha*t), y2ih=C*e^(gamma*t) …… A=1 B=22 C=-33 alpha=2 betha=-2 gamma=-2)
y1=y1h+y1ih y2=y2h+y2ih

the whole thing would be easier if u know y1(0) and y2(0) values, in that case u can use Laplapce transformation
EDIT: you can Laplacetransform using y1(0)=c1 y2(0)=c2, but without mathematica8(or sth like that) it will be really hard.

From: Hobbit
Here is what I've gotten. Its been a bit since I've done DiffEq so no guarantee they are correct :p Don't have time to bother with general solutions for #1, 2, 5. And you should at least do some yourself or you will never pass the final ;)

#3
y1 = t-sin(2t)+cos(2t)+1
y2 = 2t+6sin(2t)+cos(2t)-(1/2)

#4
y1 = -4e^(-3t)+16e^(2t)+e^(3t)-2
y2 = e^(-3t)(8e^(5t)+3)

#3 is correct, i solved it with Laplacetr.

so tough