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

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- Nov 18th 2010, 03:10 AMnepmma1st order DE and difference equation.
Solve the following differential/difference equations and show whether they are convergent

Attachment 19756 - Nov 18th 2010, 03:31 AMmr fantastic
- Nov 18th 2010, 08:27 AMnepmma
[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 - Nov 18th 2010, 11:45 AMHallsofIvy
[QUOTE=nepmma;585567] dy= -2(x- 3)dx.

Quote:

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

Then $\displaystyle y(t)- y(t-1)= -1y(t-1)+ 12$ 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.