Question 1 Identify the correct M and N for the following differential equations, then test for exactness: a) 2xyx+x'dy-0 b) 2ne'de+x'e'dy-0 c) (1-x)+(2y-x'y)dy-0 d) (x²-sin(3y))dx-3xcos(3y)dy-0 Question 2 Find , and er if all the following equations are EXACT. a) (x+y)+(2x+y)dy=0 b) (x+2y)de+(x+y)dy-0 c) (+axy-2x)de (320x¹y)dy-0 Question 3 Find the solutions for the following differential equations. a) b) (2x-x)dx-xydy-0 c) (+)+(-3)dy-0 1) (xsin 2y+e)dx+(x'cos2y + x)=0 +ycos(x))dx+(sin(x)-4y')-0 Question 4 Find the particular solution: a) (2xy +6x)dx=(x+2y)dy-0 (0)-3 b) (x-2)(x-1)dy-0 (0)-4 e) (cos(3x)+2y)de+(2x+y'ain (3x))dy-0 (0)-1
Question 1 Identify the correct M and N for the following differential equations, then test for exactness: a) 2xyx+x'dy-0 b) 2ne'de+x'e'dy-0 c) (1-x)+(2y-x'y)dy-0 d) (x²-sin(3y))dx-3xcos(3y)dy-0 Question 2 Find , and er if all the following equations are EXACT. a) (x+y)+(2x+y)dy=0 b) (x+2y)de+(x+y)dy-0 c) (+axy-2x)de (320x¹y)dy-0 Question 3 Find the solutions for the following differential equations. a) b) (2x-x)dx-xydy-0 c) (+)+(-3)dy-0 1) (xsin 2y+e)dx+(x'cos2y + x)=0 +ycos(x))dx+(sin(x)-4y')-0 Question 4 Find the particular solution: a) (2xy +6x)dx=(x+2y)dy-0 (0)-3 b) (x-2)(x-1)dy-0 (0)-4 e) (cos(3x)+2y)de+(2x+y'ain (3x))dy-0 (0)-1
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...
Related questions
Question
Transcribed Image Text:Question 1
Identify the correct M and N for the following differential equations, then test for exactness:
a) 2xyx+x'dy-0
c) x²y³dx+3x²y=0
b) 2xe dr+x'e'dy-0
c) (1-xy)+(2y-x'y)dy-0
(xsin 2y+e)dx+(x cos2y + x)dy=0
d) (x²-sin(3y))dx-3xcos(3y)dy-0
Question 2
Find a, fand er if all the following equations are EXACT.
a) (x+y)dx+(2x+y)dy=0
b) (x+2y)dx+(x+y)dy-0
c) (+axy-2x)+(3y² + 20x'y")dy-0
Question 3
Find the solutions for the following differential equations.
a) x'ydr-
b) (2x-x)dx-xydy-0
c) (ye+e)de+(-3)dy-0
d) (3x + ycos(x))dx + (sin(x)-4y')-0
=0
Question 4
Find the particular solution:
a) (2xy +6x) dx+(x+2y)dy-0 (0) 3
b) (²-2)dx+(xy+1)dy-0 (0)-4
c) (cos(3x)+2y) de+ (2x+sin(3x))=0 (0)-1
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning