Mathematica Work 1. For dy / dt = t + y , y (0) = 1, use Euler\'s Method with h
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Question
Mathematica Work
1. For dy/dt = t + y, y(0) = 1, use Euler's Method with h = 0.5 to find the approximate solution, y(2) [i.e., the y-value of the solution when t = 2]
Store all known values into variables in Mathematica:
Define the function using: f[t_, y_] := t + y
Store t0 = 0, using: t = 0
Store y0 = 1, using: y = 1
Store the final t-value, tf = 2, using: tf = 2
Store stepsize, h, using: h = 0.5
Store number of steps, n, using: n = (tf - t)/h
Find the first approximation:
Evaluate f(tn, tn) and store into variable, k, using: k = Evaluate[f[t,y]]
Find the first approximation, y, using y = y + k*h
NOTE: The first approximation is (0.5, y)
Recursive steps:
i. Find the next t, using t = t + h
ii. Find the next slope, f(t, y), using k = Evaluate[f[t,y]]
iii. Find the next approximation, y, using y = y + k*h
Repeat (n
Explanation / Answer
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