EXAMPLE 1 A separable equation Find a function that satisfies the following initial value problem. y'(t) = y'e, y(0) = }

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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EXAMPLE 1 A separable equation Find a function that satisfies the following initial
value problem.
y'(t) = y'e, y(0) = }
Transcribed Image Text:EXAMPLE 1 A separable equation Find a function that satisfies the following initial value problem. y'(t) = y'e, y(0) = }
Expert Solution
Step 1

Given

y't=y2e-t ,y0=12

Step 2

dydt=y2e-t 

dyy2=e-tdt 

Integrate both side

dyy2=e-tdt -1y=-e-t+C

Now using given condition y0=12

 

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