You have answered 3 out of 5 parts correctly.Consider the vector field i = yỉ + 5zj and function f(x, y) = 5x2 – y. In this problem we show that the flow lines of the vector field are level curves of the function f.(a) Suppose that F(t) = r(t)i+ y(t)3 is a flow line of v. Let g(t) = f(r(t)). If ř is a level curve of f(x,y), that is g(t)?g(t) = 0(b) Use the definition of f to find g. (Note that z and y are functions of t, so that your expression should involve factors of z, y, r' and y; enter z, y, z' and y in your answer rather thanz(t), y(t), r'(t) and y'(t).)g = -2 · 5xx' + 2· lyy'(c) Knowing that ř is a flow line of the vector field i, what are z' and y?z'y= 5x(d) Substituting these into your result from (b), what do you get?d = 2: (5) - 5xy+2·1·5yx(Note that this confırms our expectation from (a), showing that the flow lines are level curves of f.)

Given, Vector field v→=yi→+5xj→and function…

Answered: Consider the vector field ű = yi + 5zj…

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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Consider the vector field ű = yi + 5zj and function f(z, y) = 5z2 – y. In this problem we show that the flow lines of t (a) Suppose that #(t) = z(t)i+ y(t)j is a flow line of v. Let g(t) = f(7(t)). If # is a level curve of f(z, y), that is g'(t)? g(t) - 0 %3D