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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.
long ago, people decided to divide the day into units called hours. they choose 24 as the number of hours in one day. why is 24 a more convenient choice than 23 or 25?
4n to the power 3/2 = 8 to the power minus 1/3. find the value of n.
George worked from 7:00 A.M. to 3:30 P.M. with a 45-minute break. If George earns $10.50 per hour and does not obtain paid for his breaks, how much will he earn? (Round to the near
A company is considering whether to enter a very competitive market. In case company decided to enter in market this must either install a new forging process or pay overtime wages
A graph with a positive slope shows that the variables depicted on the axes goes in the similar directions.
David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, a
Note that there are two possible forms for the third property. Usually which form you use is based upon the form you want the answer to be in. Note as well that several of these
Illustration: Find the solution to the subsequent IVP. ty' + 2y = t 2 - t + 1, y(1) = ½ Solution : Initially divide via the t to find the differential equation in
Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre. Since Δ ADF ≅ Δ DFC ∠ADF = ∠CDF ∴ ∠ADC = 2 ∠CDF
Mary made 34 copies at the local office supply store. The copies cost $0.06 each. What was the total cost of the copies? Multiply 34 by $0.06 to ?nd out the total cost; 34 × $0
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