Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
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
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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
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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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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