can be written in differential form: where M(x, y) = M(x, y) dx + N(x, y) dy = 0 , and N(x, y) = The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by ³. equation is = C.
can be written in differential form: where M(x, y) = M(x, y) dx + N(x, y) dy = 0 , and N(x, y) = The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by ³. equation is = C.
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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![The equation
\[ y - 3y^5 = (y^4 + 4x) \, y' \]
can be written in differential form:
\[ M(x, y) \, dx + N(x, y) \, dy = 0 \]
where
\[ M(x, y) = \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, , \quad N(x, y) = \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, .\]
The term \( M(x, y) \, dx + N(x, y) \, dy \) becomes an exact differential if the left-hand side above is divided by \( y^5 \). Integrating that new equation, the solution of the differential equation is
\[ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = C. \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f1c68a1-c113-41cc-b0cf-42f2666e5687%2F03d475cb-de7d-48c2-a8eb-468d2063ae92%2Fdz58tun_processed.png&w=3840&q=75)
Transcribed Image Text:The equation
\[ y - 3y^5 = (y^4 + 4x) \, y' \]
can be written in differential form:
\[ M(x, y) \, dx + N(x, y) \, dy = 0 \]
where
\[ M(x, y) = \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, , \quad N(x, y) = \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, .\]
The term \( M(x, y) \, dx + N(x, y) \, dy \) becomes an exact differential if the left-hand side above is divided by \( y^5 \). Integrating that new equation, the solution of the differential equation is
\[ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = C. \]
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