Use Euler's method with step size 0.5 to compute the approximate y-values y(1.5) and y(2)

Question

Use Euler's method with step size 0.5 to compute the approximate y-values y(1.5) and y(2), of the solution of the initial-value problem

y'=−2+3x−2y,  y(1)=2.

y(1.5)=

y(2)=

Answer 1

Euler's method: y_n+1 = y_n + h*y_n'

In this case y(1.5) = y(1) + .5y'(1) where y'(1) = 2 + 3*1 - 2*y(1)

y(1.5) = 2 + .5(2+3-2*2) = 2.5

Now, do the same thing for the next step using the value at y(1.5), rather than y(1)

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