I In differentlal förm M dã + N dy = 0. ne equation (3x°y+ 6 cos(3a) y ?) dæ + (3x - 4y ?)dy = 0 e differential form M dx + N dy 0 is not exact. Indeed, we have M-N, For this exercise we can find an integrating factor which is a function of y alone since My-N M is a function of y alone. Namely we have µ(y) Multiplying the original equation by the integrating factor we obtain a new equation M da + N dy = 0 where %3D M %3D N = Which is exact since M, N = are equal.
I In differentlal förm M dã + N dy = 0. ne equation (3x°y+ 6 cos(3a) y ?) dæ + (3x - 4y ?)dy = 0 e differential form M dx + N dy 0 is not exact. Indeed, we have M-N, For this exercise we can find an integrating factor which is a function of y alone since My-N M is a function of y alone. Namely we have µ(y) Multiplying the original equation by the integrating factor we obtain a new equation M da + N dy = 0 where %3D M %3D N = Which is exact since M, N = are equal.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![In this problem we consider an equation in differential form M dx + N dy = 0.
The equation
(3a?y+ 6 cos(3æ) y?) dæ + (3x3 – 4y-2)dy = 0
x'y+6 cos(3x) y2) dx + (3x
4y 2)dy = 0
%3D
in differential form M dx + N dy = 0 is not exact. Indeed, we have
M,- N,
For this exercise we can find an integrating factor which is a function of y alone since
M
N
|
M
is a function of y alone.
Namely we have µ(y)
Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where
M =
N =
Which is exact since
M, =
%3D
k.
N
are equal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b6335cc-d6e6-4edb-a931-307e282480f3%2F46f17e70-9699-4405-a764-8c18fa59b377%2Fm7fzmb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In this problem we consider an equation in differential form M dx + N dy = 0.
The equation
(3a?y+ 6 cos(3æ) y?) dæ + (3x3 – 4y-2)dy = 0
x'y+6 cos(3x) y2) dx + (3x
4y 2)dy = 0
%3D
in differential form M dx + N dy = 0 is not exact. Indeed, we have
M,- N,
For this exercise we can find an integrating factor which is a function of y alone since
M
N
|
M
is a function of y alone.
Namely we have µ(y)
Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where
M =
N =
Which is exact since
M, =
%3D
k.
N
are equal.
![are equal.
This problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where
F(r, y)
Finally find the value of the constant C so that the initial condition y(0) = 1 is satisfied.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b6335cc-d6e6-4edb-a931-307e282480f3%2F46f17e70-9699-4405-a764-8c18fa59b377%2Fwioayj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:are equal.
This problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where
F(r, y)
Finally find the value of the constant C so that the initial condition y(0) = 1 is satisfied.
%3D
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