Question

I need help solving systems of linear differential equations by elimination

Answer 1

Do you understand the overall process?

Answer 2

I don't really... I understand everything about differential equations and calc up to this

Answer 3

here's an example problem:
dx/dt = 2x - y
dy/dt = x

Answer 4

So I rewrite them as Dx = 2x-y and Dy=x

Answer 5

and then I hit a wall

Answer 6

You might want to review some of your notes

you might want to construct a matrix and find the eigenvalues

this will lead you to the solution

\[\left[\begin{matrix}x(t) \\y(t) \end{matrix}\right]=\left[\begin{matrix}e^t \\e^t \end{matrix}\right]\]

Answer 7

Shoot. I haven't taken linear algebra yet :( Thanks anyway though, I'll speak to the instructor

Answer 8

the next step is to set those equations to zero; Dx-2x+y=0, Dy-x=0. then set up the system in terms of x and y\[\left(\begin{matrix}(Dx-2)x+y=0 \\ -x+Dy=0\end{matrix}\right)\] then use Kremer's Rule to solve the system, that will end up with two Second Order Differential equations, one in with respect to x and the second in respect to y. you solve those Second Order Differential equation for x(t) and y(t) respectfully, then plug back into the given equations to conform the answer.remember since this isn't a IVP it will have contsants, \[C_{1},C_{2},C_{3},C_{4}\] in the final x(t) and y(t) functions...