H1. Consider the differential equation d xcos(y) y+ (x+2) sin(y). dt First, show this equation is not exact. However, multiplying by u(x) = A(x)e* ren- ders the above differential equation exact for a specific choice of A(x). Find this A(x) and then solve the exact equation A(x)excos(y) +A(x)e*(x+2)sin(y). dy dx
H1. Consider the differential equation d xcos(y) y+ (x+2) sin(y). dt First, show this equation is not exact. However, multiplying by u(x) = A(x)e* ren- ders the above differential equation exact for a specific choice of A(x). Find this A(x) and then solve the exact equation A(x)excos(y) +A(x)e*(x+2)sin(y). dy dx
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
The "dt" in the question should be insteaded by "dx"
![H1. Consider the differential equation
xcos(y) y+ (x+2) sin(y).
d
dt
First, show this equation is not exact. However, multiplying by u(x) = A(x)e* ren-
ders the above differential equation exact for a specific choice of A(x). Find this
A(x) and then solve the exact equation
A(x)excos(y) +A(x)e*(x+2)sin(y).
dy
dx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69cce4ac-4bf6-4e6b-8636-bf160e045b58%2Fb1fa9f5f-895a-474e-8d5c-5f438caf20f6%2F1uuk67q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:H1. Consider the differential equation
xcos(y) y+ (x+2) sin(y).
d
dt
First, show this equation is not exact. However, multiplying by u(x) = A(x)e* ren-
ders the above differential equation exact for a specific choice of A(x). Find this
A(x) and then solve the exact equation
A(x)excos(y) +A(x)e*(x+2)sin(y).
dy
dx
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