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Consider the following differential equation. Let M = y5y² sin(x) - My = Nx = (x-y5+ y² sin(x)) dx = (5xy + 2y cos(x)) dy af Let = ax Is the given differential equation exact? O Yes O No f(x, y) = -x and N = 5xy¹ + 2y cos(x). Find the following partial derivatives. = y³ - y² sin(x) -x. Integrate 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) = Find the general solution of the given differential equation. (If it is not exact, enter NOT.)

Consider the following differential equation. Let M = y5y² sin(x) - My = Nx = (x-y5+ y² sin(x)) dx = (5xy + 2y cos(x)) dy af Let = ax Is the given differential equation exact? O Yes O No f(x, y) = -x and N = 5xy¹ + 2y cos(x). Find the following partial derivatives. = y³ - y² sin(x) -x. Integrate 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) = Find the general solution of the given differential equation. (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. Let M = y5y² sin(x) - My = Nx = (x-y5+ y² sin(x)) dx = (5xy + 2y cos(x)) dy af Let = ax Is the given differential equation exact? O Yes O No f(x, y) = -x and N = 5xy¹ + 2y cos(x). Find the following partial derivatives. = y³ - y² sin(x) -x. Integrate 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) = Find the general solution of the given differential equation. (If it is not exact, enter NOT.)
Transcribed Image Text:Consider the following differential equation. Let M = y5y² sin(x) - My = Nx = (x-y5+ y² sin(x)) dx = (5xy + 2y cos(x)) dy af Let = ax Is the given differential equation exact? O Yes O No f(x, y) = -x and N = 5xy¹ + 2y cos(x). Find the following partial derivatives. = y³ - y² sin(x) -x. Integrate 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) = Find the general solution of the given differential equation. (If it is not exact, enter NOT.)
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