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1) Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the...

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Advance Math

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)        (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;   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)


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