Question

1) Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion of (3) in Section 2.6

y_{n + 1} = y_n + hf(x_n, y_n)        (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 of the indicated value. Carry out the recursion of the equation

y_{n + 1} = y_n + hf(x_n, y_n)

by hand, first using h = 0.1 and then using h = 0.05.

y' = x + y², y(0) = 0;   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 a four-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)

Answer 1