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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.
Three quantities a, b and c are said to be in harmonic progression if, In this case we observe that we have to consider three terms in o
40.783-75
Euler''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.
Solve out each of the following equations. 3( x + 5)= 2 ( -6 - x ) - 2x Solution In the given problems we will explained in detail the first problem and t
Example: Suppose your football team has 10 returning athletes and 4 new members. How many ways can the coach choose one old player and one new one? Solution: There are 10 wa
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My thousandths digit is twice the tenths digit. My tenths digit is one less than the hundredths digit. If my number is 5, what my number?
6 male students and 3 female students sit around a round table. The probability that no 2 female students sit beside each other can be expressed as a/b, where a and b are coprime p
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