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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. Nx = Let af ax f(x, y) = 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. + h(y) Find the derivative of h(y). h'(y) = Is the given differential equation exact? O Yes No Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.)

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. Nx = Let af ax f(x, y) = 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. + h(y) Find the derivative of h(y). h'(y) = Is the given differential equation exact? O Yes No Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 28E
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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. Nx = af Let = 3x f(x, y) = 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. - + h(y) Find the derivative of h(y). h'(y) = No Is the given differential equation exact? Yes Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.)
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. Nx = af Let = 3x f(x, y) = 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. - + h(y) Find the derivative of h(y). h'(y) = No Is the given differential equation exact? Yes Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.)
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