Explanation Formula used: Integrating factor: The integrating factor of the First-order linear Differential equation y ′ + f ( x ) y = g ( x ) is I ( x ) = e ∫ f ( x ) d x . Calculation: The given equation is 2 x y ′ − y = 6 x 2 . Rewrite the differential equation 2 x y ′ − y = 6 x 2 into the standard form of First-order linear Differential equation y ′ + f ( x ) y = g ( x ) . 2 x y ′ − y = 6 x 2 y ′ − 1 2 x y = 3 x From the differential equation y ′ − 1 2 x y = 3 x , it is observed that f ( x ) = − 1 2 x and g ( x ) = 3 x . I ( x ) = e − 1 2 ∫ 1 x d x = e − 1 2 ln x = e ln x − 1 2 = 1 x 1 2 Thus, the integrating factor of the differential equation y ′ − 1 2 x y = 3 x is x 3 2

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Chapter 9.3, Problem 44E

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To find: The integrating factor and the general solution of the differential equation 2xy′−y=6x2.

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Chapter 9.3, Problem 43E

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The integrating factor and the general solution of the differential equation 2 x y ′ − y = 6 x 2 .

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To find: The integrating factor and the general solution of the differential equation 2xy′−y=6x2.

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