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Consider the differential equation give by
y′ = -10(y - sin t)
(a) Derive by hand exact solution that satis?es the initial condition y(0) = 1.
(b) Numerically obtain the solution to the IVP using Forward Euler with a step size of h = 0.1 from t = 0 to t = 3. Print the value of the approximate solution at time t = 3. Also plot the exact solution (with a solid line) and the approximate solution (with square markers) on the same plot.
(c) Numerically determine the relative global error,
of your approximate solution at t = 3 when h = h, h/2, h/4, h/8 and h/16.
Plot the log of the relative error vs. the log of the spacing h. Explain why this veri?es your scheme is convergent to order 1.
Sin129
Using the example provided, Evaluate the area of the shaded region in terms of π. a. 264 - 18π b. 264 - 36π c. 264 - 12π d. 18π- 264 b. The area of the shaded r
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