Typo for the first equation of 2.1.the real equation is: y'(t) = (0.5 + sint)y/5*this is not a graded assignment*. 2.1. Let y(t) be solution to population growth equation:y'(t) = (0.5 + sin t)/5%3DConsider yo to be initial condition. Find time T s.t. y(T) = 2y0-Let f(t) be solution to corresponding constant growrth equation:f'(t) = f/10Let f(0) = yo Find To s.t. f(To) = 2y0. What can you say about To and r?%3D2.2. Solvet'y' + 2ty- y = 0Hint. Consider substution z(t) = (y(t))-n where n is some non-negative integer.Find n that reduce equation to nice form.

Answered: . Let y(t) be solution to population…

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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Typo for the first equation of 2.1.

the real equation is: y'(t) = (0.5 + sint)y/5

*this is not a graded assignment*.

2.1. Let y(t) be solution to population growth equation:
y'(t) = (0.5 + sin t)/5
%3D
Consider yo to be initial condition. Find time T s.t. y(T) = 2y0-
Let f(t) be solution to corresponding constant growrth equation:
f'(t) = f/10
Let f(0) = yo Find To s.t. f(To) = 2y0. What can you say about To and r?
%3D
2.2. Solve
t'y' + 2ty- y = 0
Hint. Consider substution z(t) = (y(t))-n where n is some non-negative integer.
Find n that reduce equation to nice form.

Expert Solution

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Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.

The general solution of a differential equation contains the constant of integration. The initial condition is used to determine the constant of integration.

It is known that $\int \frac{d (g (x))}{g (x)} = \ln (g (x)) + C$ , where C is the constant of integration.