Problem 2: Find an ODE of the form + P(x)y = Q(x); y(0) = a (i.e., find P(x), Q(x) and a) whose dx solution is y = 2(sinx – cosx) + 2e¬×. %3D

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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Physical Chemistry

 

Problem 2: Find an ODE of the form
dx
+ P(x)y = Q(x); y(0) = a (i.e., find P(x), Q(x) and a) whose
%3D
solution is y = 2(sinx – cosx) + 2e¬x.
%3D
Transcribed Image Text:Problem 2: Find an ODE of the form dx + P(x)y = Q(x); y(0) = a (i.e., find P(x), Q(x) and a) whose %3D solution is y = 2(sinx – cosx) + 2e¬x. %3D
Expert Solution
Step 1

The solution to the ODE is:

y=2sinx-cosx+2e-x......(1)

At x = 0, y = a, so

a=2(sin0-cos0)+2e-0a=2(0-1)+2a=-2+2a=0

 

 

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