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2. Consider the differential equation dy dx x cos(y); to find the solution y. = A(x)e x cos(y). 2 First, show this equation is not exact. However, multiplying both sides by R(x) = A(x)e² renders the above differential equation exact for a specific choice of A(x). Show that such A(x) must satisfy the (separable!) differential equation find A(x), and then solve the exact equation dy dx A'(x) -(x + 2) sin(y). = A(x) X + A(x)eª (x + 2) sin(y) = 0

2. Consider the differential equation dy dx x cos(y); to find the solution y. = A(x)e x cos(y). 2 First, show this equation is not exact. However, multiplying both sides by R(x) = A(x)e² renders the above differential equation exact for a specific choice of A(x). Show that such A(x) must satisfy the (separable!) differential equation find A(x), and then solve the exact equation dy dx A'(x) -(x + 2) sin(y). = A(x) X + A(x)eª (x + 2) sin(y) = 0

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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2. Consider the differential equation dy dx x cos(y); to find the solution y. = A(x)e x cos(y). 2 First, show this equation is not exact. However, multiplying both sides by R(x) = A(x)e² renders the above differential equation exact for a specific choice of A(x). Show that such A(x) must satisfy the (separable!) differential equation find A(x), and then solve the exact equation dy dx A'(x) -(x + 2) sin(y). = A(x) X + A(x)eª (x + 2) sin(y) = 0
Transcribed Image Text:2. Consider the differential equation dy dx x cos(y); to find the solution y. = A(x)e x cos(y). 2 First, show this equation is not exact. However, multiplying both sides by R(x) = A(x)e² renders the above differential equation exact for a specific choice of A(x). Show that such A(x) must satisfy the (separable!) differential equation find A(x), and then solve the exact equation dy dx A'(x) -(x + 2) sin(y). = A(x) X + A(x)eª (x + 2) sin(y) = 0
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