0.246.81012(b) Find the solution of the given initial value problem.NOTE: Denote the Heaviside function by uc(t) where uc(t) = 1 if t > c and 0 otherwise.Indicate separately the value of c.%3Dy(t) =where c =(c) Use a graphing utility to view the graph of the solution.(d) Explain how the graphs of the forcing function and the solutionare related.After an initial transient, the solution Choose one Consider the following initial value problem:y(4) + 41y" + 400y = 1 – u(t);y(0) = 0, y'(0) = 0, y"(0) = 0, y"(0) = 0;(a) Sketch the graph of the forcing function on an appropriate interval.10.80.60.40.246.1012(b) Find the solution of the given initial value problem.NOTE: Denote the Heaviside function by uc(t) where uc(t) = 1 if t > c and 0 otherwise.%3DIndicate separately the value of c.y(t) =2.

We will find out the required solution.

Answered: Consider the following initial value…

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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5. Find the linearization L(x) of f at a = 0 1 f(x)%3= V2+x a = 0 %3D Select the correct answer. 1 a) L(x): V2 4V2 b) L(x) = -+ 1 4/2 c) L(x) = -- %D V2 4/2 d) L(x) = V2 – 4V2x e) none
4. Suppose you are climbing a hill whose shape is given by the equation f(x, y) 360 – x2 – 0.1y², where x and y are measured in meters. You are standing at the point P(12, 10, 206) on the hill. (NOTE: Your answers might not seem realistic for an actual hill you can climb.) - - (a) Find Vf at the point (12, 10). (b) From this point, in which direction is the slope the greatest? Give your answer as a unit vector, with all numbers exact (not decimal approxima- tions). (c) What is the rate of ascent in the direction of the greatest slope (found in part (b))? Give an exact answer (not a decimal approximation). (d) Suppose that the positive y-axis points north and the positive x-axis points east. If you walk directly southwest, will you be ascending or descending? At what rate? Give an exact answer or round your answer to three decimal places.
Let f(x) = - 4, 9(x) = r² + 4, and h(x) = 1 + 5. Without a calculator, match the functions in (a)-(f) to the descriptions in (i)–(viii). Some of the functions may match none of the descriptions. f(x) g(x) h(x) (c) y= T(1) g(z) (a) y = (b) y f(z) g(x) (e) y = h(x) h(r*) (f) y = h(x) (d) y = fE) (g) y = g(x) (h) y = f(x) - g(x) (i) Horizontal asymptote at y = 0 and one zero at z = -5. (ii) No horizontal asymptote, no zeros, and a vertical asymptote at z = -5. (iii) Zeros at z = -5, x = -2, and r = 2. (iv) No zeros, a horizontal asymptote at y = 0, and a vertical asymptote at z = -5. (v) Two zeros, no vertical asymptotes, and a horizontal asymptote at y = 1. (vi) No zeros, no vertical asymptotes, and a horizontal asymptote at y = 1. vii) Horizontal asymptote at y = -4. viii) No horizontal asymptotes, two zeros, and a vertical asymptote at z = -5.
6. There is a function x(t) = 2 - 3t+ (10)t² x (t) a. Make a {t, x(t)} axis and sketch this function on some scratch paper, or below if you can fit it. 2 4 16 38 70 112 164 226 10 16 2-3 (0) + = (10) =2 c. Solve and then sketch axes?) d² x(t) dt² 2 d² x (t) dt² 20 dt b. Solve and then sketch dx(t) for the function above (how do you label these axes?) dx (+) dt 36 -10 30 10 for the same initial function (and how should you label these 20

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