8. Determine the Green's function and solve the following problemy" + y = f(x), y(0) = 1, y'(0) = −1,(0, x < 0where f(x) = {10, 0≤x≤ 37(0, x > 3T

The given problem is y''+ y = fx, y0 = 1, y'0 =-1, where fx = 0, x<010, 0⩽x⩽3π0, x>3π

Answered: 8. Determine the Green's function and…

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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9. If f(x) + x2[f(x)]4 = 18 and f(1) = 2, find f '(1).
1. Candace tried to find the derivative of the function y = h(x)e-4f(x) but her group members disagreed with her result. What did she get right? What did she get wrong? Correct her y' = h'(x)e-4f(x) + h(x)e-4f(x) (-4) work. After figuring out her error, Candace attempted to check her solution by rearranging the right side of the equation y = h(x)e-4f(x) into a fraction and using the quotient rule to differentiate. Verify the correct solution using this method.
2 2 3 4 f(x) 7
3. Suppose that the temperature on a metal plate is given by the function T with T(x, y) = 100 - (x² +4y²) where the temperature is measured in degrees Fahrenheit and a and y are each measured in feet. Now suppose that an ant is walking on the metal plate in such a way that it walks in a straight line from the point (1, 4) to the point (5, 6). (a) Find parametric equations for the ant's a and y coordinates as it walks the line from (1,4) to (5,6) in one minute at a constant speed. (b) What can you say about dr dt and dy dt for every value of t? (c) Determine the instantaneous rate of change in temperature with respect to t that the ant is experi- encing at the moment it is halfway from (1, 4) to (5,6). Include units in your answer.

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8. Determine the Green's function and solve the following problem y" + y = f(x), y(0) = 1, y'(0) = -1, (0, x < 0 where f(x) = {10, 0≤x≤ 3 π 0. x > 3 п