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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
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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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
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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