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1. (a) Verify that P(t) = dP equation = A(C - P)P. Here a is an arbitrary constant. dt ae-CAt + 1 is a solution of the logistic differential (b) Obtain the formula for P(t) by solving the logistic differential equa- tion. (c) Solve the initial value problem P(0) = Po. dP dt = A(C - P)P,

1. (a) Verify that P(t) = dP equation = A(C - P)P. Here a is an arbitrary constant. dt ae-CAt + 1 is a solution of the logistic differential (b) Obtain the formula for P(t) by solving the logistic differential equa- tion. (c) Solve the initial value problem P(0) = Po. dP dt = A(C - P)P,

Advanced Engineering Mathematics
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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C ae-CAt +1 1. (a) Verify that P(t) dP equation = A(C - P)P. Here a is an arbitrary constant. dt = is a solution of the logistic differential (b) Obtain the formula for P(t) by solving the logistic differential equa- tion. P(0) = Po. (c) Solve the initial value problem = A(C - P)P, dP dt
Transcribed Image Text:C ae-CAt +1 1. (a) Verify that P(t) dP equation = A(C - P)P. Here a is an arbitrary constant. dt = is a solution of the logistic differential (b) Obtain the formula for P(t) by solving the logistic differential equa- tion. P(0) = Po. (c) Solve the initial value problem = A(C - P)P, dP dt
Expert Solution
Step 1

1. (a) To verify: P(t)=Ca e-C A t+1 is a solution of the logistic differential equation dPdt=AC-PP. Here a is an arbitrary constant.

 

(b) To Obtain: A formula for P(t) by solving the logistic differential equation.

 

(c) To Solve: The initial value problem dPdt=AC-PP,   P0=P0.

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