Explanation Formula used: Integrating factor: The integrating factor of a function f ( x ) is given by I ( x ) = e ∫ f ( x ) d x . Calculation: First find the solution by using an integrating factor. The given equation can be written as follows. y ′ = 2 x ( y + 1 ) y ′ = 2 x y + 2 x y ′ − 2 x y = 2 x Find the integrating factor of this first order linear equation where f ( x ) = − 2 x and g ( x ) = 2 x . I ( x ) = e ∫ − 2 x d x = e − 2 ∫ x d x = e − 2 ( x 2 2 ) = e − x 2 Multiply both sides of the equation y ′ − 2 x y = 2 x by the integrating factor. e − x 2 y ′ − 2 e − x 2 x y = 2 e − x 2 x ( e − x 2 y ) ′ = 2 e − x 2 x [ ∵ ( x y ) ′ = x y ′ + x ′ y ] Integrating on both sides, ∫ ( e − x 2 y ) ′ d x =

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 9.3, Problem 53E

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To find: The general solution of the equation y′=2x(y+1) using integrating factor and separation of variables.

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Chapter 9.3, Problem 52E

Chapter 9.3, Problem 54E

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EBK CALCULUS FOR BUSINESS, ECONOMICS, L

Ch. 9.1 - Show that y=Cx+1 is the general solution of the...Ch. 9.1 - Prob. 2MP Ch. 9.1 - Prob. 3MP Ch. 9.1 - Prob. 4MP Ch. 9.1 - Prob. 5MP Ch. 9.1 - Prob. 1ED Ch. 9.1 - Prob. 2ED Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E

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The general solution of the equation y ′ = 2 x ( y + 1 ) using integrating factor and separation of variables.

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To find: The general solution of the equation y′=2x(y+1) using integrating factor and separation of variables.

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