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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.)

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. 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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