Finding the Operational Determinant for a Differential Equation

[jinksys]

Homework Statement

This is a problem in differential equations.

Find the operational determinant and solve the equation.

x'= 4x + y + 2t

y' = -2x + y

Homework Equations

The Attempt at a Solution

I'm at a total loss. All the examples in the book have problems with the form:

(D - 4)x + 3y = 0
-6x + (D + 7)y = 0

Nothing like what I have, and certainly nothing with x,y, AND t. That t really throws me off.

 

[korican04]

Homework Statement

This is a problem in differential equations.

Find the operational determinant and solve the equation.

x'= 4x + y + 2t

y' = -2x + y

Homework Equations

The Attempt at a Solution

I'm at a total loss. All the examples in the book have problems with the form:

(D - 4)x + 3y = 0
-6x + (D + 7)y = 0

Nothing like what I have, and certainly nothing with x,y, AND t. That t really throws me off.

First when doing these problems put all the xs and ys on one side of the equations.
So first you'll have
x'-4x - y = 2t
2x + y' - y = 0

Now factor the differential operator "D" from the differentials. (I'm assuming x and y are functions of t)

(D-4)x + 3y = 2t
2x + (D-1)y = 0

This gives you a way to find the operational determinant. To solve for a general solution you'll have to work a little more.
Try the problem now..

 

[jinksys]

Thanks, it's much more clear now. I'll give the problem another try later.