# Thread: 1st order DE and difference equation.

1. ## 1st order DE and difference equation.

Solve the following differential/difference equations and show whether they are convergent

2. Originally Posted by nepmma
Solve the following differential/difference equations and show whether they are convergent
Please type your questions out so that we do not have to opeb attachments.

What have you tried and where are you stuck?

3. [QUOTE=nepmma;585464]Solve the following differential/difference equations and show whether they are convergent

a) dy/dx=-3x-9
b) change in y at time t = -2(y at time (t-1))+12

i am stuck on part b as it includes the time element

4. [QUOTE=nepmma;585567]
Originally Posted by nepmma
Solve the following differential/difference equations and show whether they are convergent

a) dy/dx=-3x-9
dy= -2(x- 3)dx.

b) change in y at time t = -2(y at time (t-1))+12

i am stuck on part b as it includes the time element
"Change in y" over what interval? $\Delta t= 1$?
Then $y(t)- y(t-1)= -1y(t-1)+ 12$ so that math]y(t)= -2y(t-1)+ 12[/tex].

In order to solve that you would need to know y(t) over some initial interval, say t= 0 to t= 1.

Given that y(t)= f(t) for t= 0 to t= 1, y(t)= 12- 2f(t) for t= 1 to 2, y(t)= 12- 24- 4f(t)= -12- 4f(t) for t= 2 to t= 3, y(t)= 12- (-24- 8f(t))= 36+ 4f(t) for t= 3 to 4, etc.