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Question 1. Find the solution of the following differential equations (i) cos²x sin x + (cos³x)y = 1

Question 1. Find the solution of the following differential equations (i) cos²x sin x + (cos³x)y = 1

Calculus: Early Transcendentals
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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Question 1. Find the solution of the following differential equations (i) cos² r sin 2+ (cos³x)y = 1 (ii) y-2xy = 1, y(1) = 1 (Revise Fundamental theorem of Calculus and see definition for erf(x)), (iii) y¹/2+³/2 = 1, y(1) = 1/ (iv) x=yer/v- x (v) eye-y+e-22-y Question 2. Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (zo, yo) in the region. (i) = y2/3 (ii)=√√ry Question 3. Discuss the existence and uniqueness of a solution of the initial value problem, (a) xy - 4y = xe", for (i) y(0) = 0, (ii) y(ro) yo, 20 > 0, yo > 0. = (b) = y, y(0) = 0. Question 4. Find function M(x, y) so that the given differential equation is exact M(x,y)dr+(new. Solve the obtained exact differential equation. -1) dy + 2xy + dy = 0,
Transcribed Image Text:Question 1. Find the solution of the following differential equations (i) cos² r sin 2+ (cos³x)y = 1 (ii) y-2xy = 1, y(1) = 1 (Revise Fundamental theorem of Calculus and see definition for erf(x)), (iii) y¹/2+³/2 = 1, y(1) = 1/ (iv) x=yer/v- x (v) eye-y+e-22-y Question 2. Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (zo, yo) in the region. (i) = y2/3 (ii)=√√ry Question 3. Discuss the existence and uniqueness of a solution of the initial value problem, (a) xy - 4y = xe", for (i) y(0) = 0, (ii) y(ro) yo, 20 > 0, yo > 0. = (b) = y, y(0) = 0. Question 4. Find function M(x, y) so that the given differential equation is exact M(x,y)dr+(new. Solve the obtained exact differential equation. -1) dy + 2xy + dy = 0,
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