For the equation y 3 ty y01 find the approximate values of

For the equation: y\'= 3 + t-y, y(0)-1, find the approximate values of the solution = 0.1, 0.2, 0.3, 0.4 using Euler method with h = 0.1.

Solution

Solution: We know the formula y_n = hf(t_n-1, y_n-1)+y_n-1, where here f(t, y) = 3+t-y. So y_n = 0.3+0.1t_n-1 +0.9y_n-1. This allows us to build the following table :

  

i	ti	yi
0	0	1
1	0.1	1.2
2	0.2	1.39
3	0.3	1.571
4	0.4	1.7439