# 1st order DE and difference equation.

• Nov 18th 2010, 03:10 AM
nepmma
1st order DE and difference equation.
Solve the following differential/difference equations and show whether they are convergent
Attachment 19756
• Nov 18th 2010, 03:31 AM
mr fantastic
Quote:

Originally Posted by nepmma
Solve the following differential/difference equations and show whether they are convergent
Attachment 19756

Please type your questions out so that we do not have to opeb attachments.

What have you tried and where are you stuck?
• Nov 18th 2010, 08:27 AM
nepmma
[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 AM
HallsofIvy
[QUOTE=nepmma;585567]
Quote:

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.

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
"Change in y" over what interval? \$\displaystyle \Delta t= 1\$?
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.