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Consider the following differential equation. (x - y + y² sin(x)) dx = (6xy5 + 2y cos(x)) dy

Consider the following differential equation. (x - y + y² sin(x)) dx = (6xy5 + 2y cos(x)) dy

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. (x - y + y² sin(x)) dx = (6xy5 + 2y cos(x)) dy Let M = y6 - y² sin(x) - x and N = 6xy5 + 2y cos(x). Find the following partial derivatives. = My N. = Is the given differential equation exact? Yes No af Let =y6y² sin(x) - x. Integrate this partial derivative with respect to x, letting h(y) be an unknown function in y. əx f(x, 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. (x - y + y² sin(x)) dx = (6xy5 + 2y cos(x)) dy Let M = y6 - y² sin(x) - x and N = 6xy5 + 2y cos(x). Find the following partial derivatives. = My N. = Is the given differential equation exact? Yes No af Let =y6y² sin(x) - x. Integrate this partial derivative with respect to x, letting h(y) be an unknown function in y. əx f(x, 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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