1) Use Euler's method to obtain a four-decimal approximation ofthe indicated value. Carry out the recursion of (3) in Section2.6
yn + 1 = yn + hf(xn,yn)Â Â Â Â Â Â Â Â (3)
by hand, first using h = 0.1 and then using h = 0.05.
y' = 2x − 3y + 1, y(1) = 4;   y(1.2)
| y(1.2) | ≈ | (h = 0.1) |
| y(1.2) | ≈ | (h = 0.05) |
2)Use Euler's method to obtain a four-decimal approximation ofthe indicated value. Carry out the recursion of the equation
yn + 1 = yn + hf(xn,yn)
by hand, first using h = 0.1 and then using h = 0.05.
y' = x + y2, y(0) = 0;Â Â Â y(0.2)
| y(0.2) | ≈ | (h = 0.1) |
| y(0.2) | ≈ | (h = 0.05) |
3) Use a numerical solver and Euler's method to obtain afour-decimal approximation of the indicated value. First use
h = 0.1 and then use h = 0.05.
y' = e−y, y(0) = 0;   y(0.5)
| y(0.5) | ≈ | (h = 0.1) |
| y(0.5) | ≈ | (h = 0.05) |
