af Əx Recall that a differential equation of the form M(x, y) dx + N(x, y) dy = 0 is exact if there is a region R of the xy-plane such that there exists a function f(x, y) defined on R such that = M(x, y) and af ду = N(x, y). By Theorem 2.4.1, the existence of the function f is equivalent to the conditions that M and N are continuous on a rectangular region a< x < b, c
af Əx Recall that a differential equation of the form M(x, y) dx + N(x, y) dy = 0 is exact if there is a region R of the xy-plane such that there exists a function f(x, y) defined on R such that = M(x, y) and af ду = N(x, y). By Theorem 2.4.1, the existence of the function f is equivalent to the conditions that M and N are continuous on a rectangular region a< x < b, c
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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Please answer the question below ty.
![af
Recall that a differential equation of the form M(x, y) dx + N(x, y) dy = 0 is exact if there is a region R of the xy-plane such that there exists a function f(x, y) defined on R such that = M(x, y) and
?x
af
ду
= N(x, y).
By Theorem 2.4.1, the existence of the function f is equivalent to the conditions that M and N are continuous on a rectangular region a < x < b, c < y < d and the following partial derivatives are equal.
ƏM ƏN
ду ?х
We are given a differential equation and must rewrite it in the form M(x, y) dx + N(x, y) dy = 0.
x dy + y -
Find the functions M and N.
M(x, y) =
=
N(x, y) =
xex.
dy
dx
x dy =
- 8xex - 6x²
= 8xex - y + 6x²
(8xex - y + 6x²) dx
- 6x² dx = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb52044d-d588-4d60-8413-960f544d05a0%2Fb228bfce-92e6-4d17-bda5-ff4157ab8f3a%2F5z36eba_processed.jpeg&w=3840&q=75)
Transcribed Image Text:af
Recall that a differential equation of the form M(x, y) dx + N(x, y) dy = 0 is exact if there is a region R of the xy-plane such that there exists a function f(x, y) defined on R such that = M(x, y) and
?x
af
ду
= N(x, y).
By Theorem 2.4.1, the existence of the function f is equivalent to the conditions that M and N are continuous on a rectangular region a < x < b, c < y < d and the following partial derivatives are equal.
ƏM ƏN
ду ?х
We are given a differential equation and must rewrite it in the form M(x, y) dx + N(x, y) dy = 0.
x dy + y -
Find the functions M and N.
M(x, y) =
=
N(x, y) =
xex.
dy
dx
x dy =
- 8xex - 6x²
= 8xex - y + 6x²
(8xex - y + 6x²) dx
- 6x² dx = 0
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