1. For the system the curve Y() = (cos t, sint) is a solution. This solution is periodic. Its initial position is Y(0) = (1,0), and it returns to this position when t = 2r. So Y(2r) = (1,0) and Y(t + 2r) = Y(t) for all t. (a) Check that Y(t) = (cost, sin t) is a solution. (b) Use Euler's method with step size 0.5 to approximate this solution, and check how close the approximate solution is to the real solution when t= 4, t= 6, and i 10.
1. For the system the curve Y() = (cos t, sint) is a solution. This solution is periodic. Its initial position is Y(0) = (1,0), and it returns to this position when t = 2r. So Y(2r) = (1,0) and Y(t + 2r) = Y(t) for all t. (a) Check that Y(t) = (cost, sin t) is a solution. (b) Use Euler's method with step size 0.5 to approximate this solution, and check how close the approximate solution is to the real solution when t= 4, t= 6, and i 10.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Section 2.5
Problem 2,
Only (a. & b.) please
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