Explanation Using Separation of Variables, separate the x and y terms and integrate to obtain the solution. Given: y ' − e x + y = 0 Calculation: Given y ' − e x + y = 0 Thus, d y d x = e x + y => e − y d y = e x d x Integrating on both sides yields ∫ e − y d y = ∫

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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(12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.

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The general solution using Separation of Variables.

Solution Summary: The author explains how to determine the general solution using Separation of Variables. Separate the x and y terms and integrate to obtain the solution.

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