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As the equation is exact, there is a function f such that. = M(x, y) and = N(x, y). af ax af ду To find the function f, first take the integral of M with respect to x. Note the middle term requires the use of integration by parts. af əx -J = [M(x, y) dx = f(x- (y - 8xe* - 6x²) dx +(([ = xy + f(x, y) = dx -(C xe ) - 2x3 -2x³ + h(y)

As the equation is exact, there is a function f such that. = M(x, y) and = N(x, y). af ax af ду To find the function f, first take the integral of M with respect to x. Note the middle term requires the use of integration by parts. af əx -J = [M(x, y) dx = f(x- (y - 8xe* - 6x²) dx +(([ = xy + f(x, y) = dx -(C xe ) - 2x3 -2x³ + 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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Please answer step 3 ty.

As the equation is exact, there is a function f such that = M(x, y) and = N(x, y). af əx af ay To find the function f, first take the integral of M with respect to x. Note the middle term requires the use of integration by parts. = [ of dx f(x, y) = = M(x, y) dx -for - 8xe* - 6x²) dx = xy + +(([ 1xex) - 2 The unknown function h in the variable y functions as a constant of integration in the integration with respect to x. When taking the partial derivative of f(x, y) with respect to x, the derivative of the term h(y) is 0. xex-2x³ + h(y)
Transcribed Image Text:As the equation is exact, there is a function f such that = M(x, y) and = N(x, y). af əx af ay To find the function f, first take the integral of M with respect to x. Note the middle term requires the use of integration by parts. = [ of dx f(x, y) = = M(x, y) dx -for - 8xe* - 6x²) dx = xy + +(([ 1xex) - 2 The unknown function h in the variable y functions as a constant of integration in the integration with respect to x. When taking the partial derivative of f(x, y) with respect to x, the derivative of the term h(y) is 0. xex-2x³ + h(y)
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