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Help Solving a System Of DEQ'sby ajohncock
Tags: solving 
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#1
Mar2309, 04:25 PM

P: 7

Hi Guys,
I'm tying to solve a system of equations. I know I need to operate on the top and the bottom both in order to isolate the X's and Y's, but I can't seem to figure what to operate on them with. Here are the equations, any help is appreciated. Thanks D^{2}x  Dy=t (D+3)x + (D+3)y=2 I should be able to finish solving it if I can just get them in the forms I need. Edit: I have a feeling this is going to seem really obvious and easy when I see it. But I am just getting in to Differential Equations, so I am new at this stuff. 


#2
Mar2309, 04:30 PM

P: 74

what about if you substitute Dy from (1) into (2), then you have a second order diffential equation in form of x and t. I believe x and y are function of t



#3
Mar2309, 04:53 PM

P: 7

If I do that then I get D^{2}x + Dx + 3x  t + 3y = 2
Then I don't know how to deal with the t + 3y Thanks for the idea though. I hadn't thought of it. Edit: After another look you could then write it as D^{2}x + Dx + 3x = t  3y + 2 But I still don't know what to do with it from here. I can solve the associated homogeneous equation, but then I still don't know what to do with the y on the right side. I think I have to get rid of either y or x entirely before I can solve for x(t) or y(t). 


#4
Mar2309, 05:14 PM

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Help Solving a System Of DEQ's
Hi ajohncock! Welcome to PF!



#5
Mar2309, 05:22 PM

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tinytim, are you asserting that he should be able to solve a single equation in two unknowns?
D^{2}x  Dy=t (D+3)x + (D+3)y=2 If you "multiply" the first equation by D3 and the second equation by D you get D^{2}(D3)x D(D3)y= (D3)t= 3t D(D+3)x+ D(D3)y= 0 and then adding eliminates y: D^{2}(D3)x+ D(D3)x= 3t or D(D+1)(D3)x= 3t. Solve that equation for x, then put that x into D^{2}x Dy= t and solve that equation for y. 


#6
Mar2309, 05:50 PM

P: 7

I then added the equations and come up with this: D^{2}x(D+3) + D(D+3)x = 2D + 3t + tD Simplified that is D^{3}x + 4D^{2}x + 3Dx = 2D + 3t + Dt Which does get rid of the y, but now I am unsure what to do with the right side. This is frustrating. 


#8
Mar2309, 06:05 PM

P: 7




#10
Mar2309, 06:14 PM

P: 7

Dy = Dx  3x  3y +2 Which is all fine and good except for the 3y. Which poses a problem when substituted back into the first equation. 


#12
Mar2309, 06:22 PM

P: 7




#13
Mar2309, 06:37 PM

P: 7

Man i've been looking at this and manipulating it for too long. I've got nothing! It's the right side I don't know how to deal with.



#15
Mar2409, 02:16 PM

P: 74




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