Explanation Verify the identity given and then integrate to obtain the general solution of y ' + 2 x y = x Given: α ( x ) = e x 2 Calculation: Given α ( x ) = e x 2 Hence ( α ( x ) y ) ' = ( e x 2 y ) ' = 2 x e x 2 y + e x 2 y ' = e x 2 ( 2 x y + y ' ) = α ( x ) ( 2 x y + y ' ) If we multiply both sides by α ( x ) , we get α (...

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ISBN: 9781319050733

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Publisher: MAC HIGHER

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Differential Equations

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Chapter 10.5, Problem 3E

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To verify the identity $(α (x) y)' = α (x) (y' + 2 x y)$ and explain how it is used to find the general solution of $y' + 2 x y = x$

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Chapter 10.5, Problem 2E

Chapter 10.5, Problem 4E

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To verify the identity ( α ( x ) y ) ' = α ( x ) ( y ' + 2 x y ) and explain how it is used to find the general solution of y ' + 2 x y = x

Solution Summary: The author explains how to verify the identity given and integrate to obtain the general solution of y.

Concept explainers

Videos

To verify the identity $(α (x) y)' = α (x) (y' + 2 x y)$ and explain how it is used to find the general solution of $y' + 2 x y = x$

Want to see the full answer?

Chapter 10 Solutions

To verify the identity ( α ( x ) y ) ' = α ( x ) ( y ' + 2 x y ) and explain how it is used to find the general solution of y ' + 2 x y = x

Solution Summary: The author explains how to verify the identity given and integrate to obtain the general solution of y.

Concept explainers

Videos

To verify the identity (α(x)y)'=α(x)(y'+2xy) and explain how it is used to find the general solution of y'+2xy=x

Want to see the full answer?

Chapter 10 Solutions

To verify the identity $(α (x) y)' = α (x) (y' + 2 x y)$ and explain how it is used to find the general solution of $y' + 2 x y = x$