00:01
In this problem, we are given this differential equation y ' equal to 40 plus exponential minus t y with the initial condition y0 equal to 0.
00:13
And we are going to estimate the values of y at t equal to 0 .1, 0 .2, 0 .3 and 0 .4 using the earlier method with a step size of h equal to 0 .05.
00:29
We are going to keep 8 decimal places when we are working on the solutions but we will report the final answers with 5 decimal places.
00:40
Let's remember this earlier method.
00:44
When we are given some equation as y ' equal to some function of t and y, we write yn plus 1 equal to yn plus h times f of t, tn and yn.
01:03
Most of the time we simply indicate this guy by f sub n.
01:11
Here n goes like 0, 1, 2 and so on.
01:16
Now we know the f function here and we have the initial values t0 equal to 0 and y0 equal to 0.
01:27
So with that we are going to prepare the following table.
01:30
I will show the values of n, tn, yn, fn and finally yn plus 1.
01:45
So we always start with the t column because we know the values of our grid.
01:52
0, 0 .05, 0 .1, 0 .15 all the way up to 0 .4.
01:59
Then we will write down the n values and we know the first value of y...