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Consider the following differential equation. (sin(y) – y sin(x)) dx + (cos(x) + x cos(y) – y) dy = 0 Let M = sin(y) - y sin(x) and N = cos(x) + x cos(y) - y. Find the following partial derivatives. M, = cos (y) – sin (x) Ny = -sin (x) + cos(y) af Let = sin(y) - y sin(x). Integrate each term of this partial derivative with respect to x, letting h(y) be an unknown function in y. ax f(x, y) = x sin (y) +y cos(x) + h(y) Find the derivative of h(y).

Consider the following differential equation. (sin(y) – y sin(x)) dx + (cos(x) + x cos(y) – y) dy = 0 Let M = sin(y) - y sin(x) and N = cos(x) + x cos(y) - y. Find the following partial derivatives. M, = cos (y) – sin (x) Ny = -sin (x) + cos(y) af Let = sin(y) - y sin(x). Integrate each term of this partial derivative with respect to x, letting h(y) be an unknown function in y. ax f(x, y) = x sin (y) +y cos(x) + h(y) Find the derivative of h(y).

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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Consider the following differential equation. (sin(y) – y sin(x)) dx + (cos(x) + x cos(y) – y) dy = 0 Let M = sin(y) - y sin(x) and N = cos(x) + x cos(y) – y. Find the following partial derivatives. cos(y) – sin (x) M, = Ny = -sin(x) + cos(y) af Let = sin(y) – y sin(x). Integrate each term of this partial derivative with respect to x, letting h(y) be an unknown function in y. ax f(x, y) = x sin (y) +y cos(x) + h(y) Find the derivative of h(y). h'(y) = -y Is the given differential equation exact? O Yes O No Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) NOT Need Help? Read It
Transcribed Image Text:Consider the following differential equation. (sin(y) – y sin(x)) dx + (cos(x) + x cos(y) – y) dy = 0 Let M = sin(y) - y sin(x) and N = cos(x) + x cos(y) – y. Find the following partial derivatives. cos(y) – sin (x) M, = Ny = -sin(x) + cos(y) af Let = sin(y) – y sin(x). Integrate each term of this partial derivative with respect to x, letting h(y) be an unknown function in y. ax f(x, y) = x sin (y) +y cos(x) + h(y) Find the derivative of h(y). h'(y) = -y Is the given differential equation exact? O Yes O No Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) NOT Need Help? Read It
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