Also find the solution of the differential equation that satisfies the initial condition y(1)=3(simplify as much as possible) find the solution of the differential equation that satisfies the initial condition y(3)= 1 (simplify as much as possible)

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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Also find the solution of the differential equation that satisfies the initial condition y(1)=3(simplify as much as possible) find the solution of the differential equation that satisfies the initial condition y(3)= 1 (simplify as much as possible)
rehtlar equadon.
Scholarship Ameri. bio 1
(b) Illustrate part (a) by graphing several members of the family of solutions on a common screen.
y
4
3
2
2
4.
6.
8
10
-10
-8
-6
-4
-1
O-2/
10
-8
-6
6
10
1
-1
Transcribed Image Text:rehtlar equadon. Scholarship Ameri. bio 1 (b) Illustrate part (a) by graphing several members of the family of solutions on a common screen. y 4 3 2 2 4. 6. 8 10 -10 -8 -6 -4 -1 O-2/ 10 -8 -6 6 10 1 -1
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MY NOTES
(a) Show that every member of the family of functions y = (4 In(x) + C)/x, x > 0, is a solution of the differential equation xy' + xy = 4. (Simplify as much as possible.)
ASK YOUR TEACHER
y - 4 In(x) + C
Y - 4x: (1/x) - (4 In(x) +C)
x2
LHS = xy' + xy = x2.
+ x.4 In(x) t C
+ 4 In(x) + C =
- RHS,
so y is a solution of the differential equation.
Transcribed Image Text:Used MY NOTES (a) Show that every member of the family of functions y = (4 In(x) + C)/x, x > 0, is a solution of the differential equation xy' + xy = 4. (Simplify as much as possible.) ASK YOUR TEACHER y - 4 In(x) + C Y - 4x: (1/x) - (4 In(x) +C) x2 LHS = xy' + xy = x2. + x.4 In(x) t C + 4 In(x) + C = - RHS, so y is a solution of the differential equation.
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