Can someone help me solve this easy algebra Question?
I know most of you Basiler's are scholars and math genius's going to Harvard and Princeton. So this question will be cake.
I need to find the general solution of this set of simultaneous differential equations. The set is:
(D+2)x + (D-1)y = 0
(2D+3)x + (3D+1)y= sin2t
November 1, 2013
9 Comments • Newest first
@Momo123: yee
[quote=9Hades9]@Momo123
Solution by -Cramer's rule :
(D+2)x + (D-1)*y = 0
(2D+3)x + (3D+1)*y= sin2t
delta:
|D+2 D-1 |
|2D+3 3D+1| = (D+2)*(3D+1)-(D-1)*(2D+3) = 3D^2+D +6D +2 -2D^2-3D+2D+3 = D^2 + 6D + 5
Lets mark this with A:
|0 D-1 |
|sin2t 3D+1| = -(D-1)*sin2t
Lets mark this with B:
|D+2 0 |
|2D+3 sin2t| = (D+2)*sin2t
So: x = A/delta,
and y = B/delta.
correct me if im wrong
i was just too lazy to go on...[/quote]
well your not really looking for x and y, you are trying to find general solution, but you are right so far. So you will get
D^2+6D+5 = -(D-1)*sin2t
D^2+6D+2= (D+2)*sin2t
which when you distribute you should get
D^2+6D+5= -2cost2t + sin2t
D^2+6D+5= 2cost2t + 2sin2t
then you make the left side the complimentary solution which will be (D^2+6D+5) = (D+1)(D+5) which makes the roots -1,-5
so it will be xc= c1e^-t + c2e^ -5t + X and yc= c1e^-t + c2e^ -5t + Y
the capital X and Y are the ride side of the equations which you have to find the particular solution to
so I think you can use Acosx + Bsinx for the particular, and then take derivative and plug into Acosx + Bsinx
then once you get capital X and Y, add to complimentary to get general solution
and... then take derivative of it and plug back into original equation
I hate differential equations lol...
mathway.com is your answer.
@Momo123
Solution by -Cramer's rule :
(D+2)x + (D-1)*y = 0
(2D+3)x + (3D+1)*y= sin2t
delta:
|D+2 D-1 |
|2D+3 3D+1| = (D+2)*(3D+1)-(D-1)*(2D+3) = 3D^2+D +6D +2 -2D^2-3D+2D+3 = D^2 + 6D + 5
Lets mark this with A:
|0 D-1 |
|sin2t 3D+1| = -(D-1)*sin2t
Lets mark this with B:
|D+2 0 |
|2D+3 sin2t| = (D+2)*sin2t
So: x = A/delta,
and y = B/delta.
correct me if im wrong
i was just too lazy to go on...
Substitute D=2, X=1, Y=-4
I got -21=sin2t..but im prob wrong.
Edit:
I did this in 2 different ways, and i got the same answer: -21=sin2t.
I'm not math genius or anything..
Yeah, nevermind.
I hated diffeq.
I've never done differential equations but I can tell you the plural of "genius" is "geniuses."
[quote=JekutoNightra]6. Possibly even 7.[/quote]
after you take cramer's rule of each one, simplify it, and take the complimentary and particular function and add them to the general solution and plug it back in to the original equation, shouldn't you get a bigger number? Then again... you are a math scholar so you're probably right
6. Possibly even 7.