Question

(3) Consider the differential equation (x + sin y) dx + (x cos y - 2y) (a) Determine whether the above equation is exact. (b) If the equation is not exact, find an integrating factor. If the equation is exact, skip this step and go on to (c). (c) Solve the equation using the method of exact solutions, using the integrating factor from (b) if necessary.

          (3) Consider the differential equation
(x + sin y) dx + (x cos y - 2y)
(a) Determine whether the above equation is exact.
(b) If the equation is not exact, find an integrating factor. If the equation is exact, skip this step and go on to (c).
(c) Solve the equation using the method of exact solutions, using the integrating factor from (b) if necessary.

(3) Consider the differential equation
(x + sin y) dx + (x cos y - 2y)
(a) Determine whether the above equation is exact.
(b) If the equation is not exact, find an integrating factor. If the equation is exact, skip this step and go on to (c).
(c) Solve the equation using the method of exact solutions, using the integrating factor from (b) if necessary.

Added by Purificaci-N P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Aman Gupta

Step 1

To check if the equation is exact, we need to see if the partial derivative of the first term with respect to y is equal to the partial derivative of the second term with respect to x. ∂(2 + siny)/∂y = cosy ∂(x cosy - 2y)/∂x = cosy Since the partial derivatives Show more…

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3) Consider the differential equation (x + sin y) dx + (x cos y - 2y) (a) Determine whether the above equation is exact. (b) If the equation is not exact, find an integrating factor. If the equation is exact, skip this step and go on to (c). (c) Solve the equation using the method of exact solutions, using the integrating factor from (b) if necessary.