# Help Solving a System Of DEQ's

by ajohncock
Tags: solving
 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 D2x - 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.
 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
 P: 7 If I do that then I get D2x + 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 D2x + 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).
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PF Gold
P: 26,105

## Help Solving a System Of DEQ's

Hi ajohncock! Welcome to PF!
 Quote by ajohncock (D+3)x + (D+3)y=2
erm … can't you just solve this on its own?
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,705 tiny-tim, are you asserting that he should be able to solve a single equation in two unknowns? D2x - Dy=t (D+3)x + (D+3)y=2 If you "multiply" the first equation by D-3 and the second equation by D you get D2(D-3)x- D(D-3)y= (D-3)t= -3t D(D+3)x+ D(D-3)y= 0 and then adding eliminates y: D2(D-3)x+ D(D-3)x= -3t or D(D+1)(D-3)x= -3t. Solve that equation for x, then put that x into D2x- Dy= t and solve that equation for y.
P: 7
 Quote by HallsofIvy If you "multiply" the first equation by D-3 and the second equation by D you get D2(D-3)x- D(D-3)y= (D-3)t= -3t D(D+3)x+ D(D-3)y= 0 and then adding eliminates y: D2(D-3)x+ D(D-3)x= -3t or D(D+1)(D-3)x= -3t. Solve that equation for x, then put that x into D2x- Dy= t and solve that equation for y.
The problem with this is that, the part I BOLDED is actually (D+3) in the original equation. However that may be on the right track. I tried multiplying the top by (D+3) and the bottom by D.

I then added the equations and come up with this:

D2x(D+3) + D(D+3)x = 2D + 3t + tD

Simplified that is D3x + 4D2x + 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.
HW Helper
Thanks
PF Gold
P: 26,105
 Quote by ajohncock (D+3)x + (D+3)y=2
solution … ?
P: 7
 Quote by tiny-tim solution … ?
Haha, I wish I knew what you meant by that.
 Sci Advisor HW Helper Thanks PF Gold P: 26,105 re-arrange it!
P: 7
 Quote by tiny-tim re-arrange it!
I assume you mean to solve the equation for Dy and substitute that back into the other equation. But when I solve it for Dy I get:

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.
HW Helper
Thanks
PF Gold
P: 26,105
 Quote by ajohncock I assume you mean to solve the equation for Dy …
how is that re-arranging it?
P: 7
 Quote by tiny-tim how is that re-arranging it?
Haha, maybe I'm not as math savvy as I thought. I guess I don't know what you mean by re-arrange it.
 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.
 Sci Advisor HW Helper Thanks PF Gold P: 26,105 just got up … (D+3)(x + y) = 2 ?
P: 74
 Quote by ajohncock If I do that then I get D2x + Dx + 3x - t + 3y = 2 Then I don't know how to deal with the -t + 3y
since y is a function of t and x then if Dy = (D^2)x -t, you can apply integration so that you now obtain what is called integro-differential equation in form of x and t

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