Numerical Mathods for Systems

[bearej50]

x' = x + 2y, x(0) = 0, y' = x + e^-t, y(0) = 0; x(t) = (1/9)(2e^(2t) - 2e^-t - 6te^-t), y(t) = (1/9)(e^(2t) - e^-t + 6te^-t)

An initial value problem and its exact solution are given. Use the Runge-Kutta method with step sizes h = 0.1 and h = 0.05 to approximate to five decimal places the values x(1) and y(1).

I have a TI-89 calculator with the proper programs to solve this problem. I am having trouble getting this problem started because of the t in "y' = x + e^-t". Can anyone get me past this???

 

[tkhunny]

Can you voice what it is about that that is bothering you?

Both x and y are fucntions of t.

Perhaps it would be of benefit to rewrite the problem a little.

Rather than y' = x + e^(-t), maybe y' = (1/9)(2e^(2t) - 2e^-t - 6te^-t) + e^(-t) would make more sense.