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Given the following first-order linear differential equation: dv 32 = dt V v-1. е a) Write the given first-order LDE in standard form. b) Solve for the general solution of your answer in part (a) using method of solution for first-order linear differential equations. Express your answer in explicit form. c) Solve for the particular solution of your result in part (b) assuming zero initial conditions, i.e., v(0) = 0. d) Solve for if the final value of your answer in part (c) is equal to 128, i.e., lim v(t) = 128. t→∞0

Given the following first-order linear differential equation: dv 32 = dt V v-1. е a) Write the given first-order LDE in standard form. b) Solve for the general solution of your answer in part (a) using method of solution for first-order linear differential equations. Express your answer in explicit form. c) Solve for the particular solution of your result in part (b) assuming zero initial conditions, i.e., v(0) = 0. d) Solve for if the final value of your answer in part (c) is equal to 128, i.e., lim v(t) = 128. t→∞0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 1CR
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Given the following first-order linear differential equation: dv dt V v-1. 32 е a) Write the given first-order LDE in standard form. b) Solve for the general solution of your answer in part (a) using method of solution for first-order linear differential equations. Express your answer in explicit form. c) Solve for the particular solution of your result in part (b) assuming zero initial conditions, i.e., v(0) = 0. d) Solve for lif the final value of your answer in part (c) is equal to 128, i.e., lim v(t) = 128. t-00
Transcribed Image Text:Given the following first-order linear differential equation: dv dt V v-1. 32 е a) Write the given first-order LDE in standard form. b) Solve for the general solution of your answer in part (a) using method of solution for first-order linear differential equations. Express your answer in explicit form. c) Solve for the particular solution of your result in part (b) assuming zero initial conditions, i.e., v(0) = 0. d) Solve for lif the final value of your answer in part (c) is equal to 128, i.e., lim v(t) = 128. t-00
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