Explanation Given information: The slope of the curve d y d x = y − x 3 y − x . The point ( 2 , 1 ) . Calculation: The slope of the curve is d y d x = y − x 3 y − x which gives the differentialequation ( y − x ) d x − ( 3 y − x ) d y = 0 . Compare the above equation with M d x + N d y = 0 to get M = ( y − x ) and N = − ( 3 y − x ) . Now, ∂ M ∂ y = ∂ ( y − x ) ∂ y = 1 ∂ N ∂ x = ∂ ( − ( 3 y − x ) ) ∂ x = − ( − 1 ) = 1 As, ∂ M ∂ y = ∂ N ∂ x the equation ( y − x ) d x − ( 3 y − x ) d y = 0 is exact. Now, f ( x , y ) = ∫ N ( x , y ) d y = ∫ − ( 3 y − x ) d y = x y − 3 y 2 2 + g ( x ) Also, f x ( x , y

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ISBN: 9781337275378

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 16.1, Problem 43E

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To calculate: An equation of the curve with the slope dydx=y−x3y−x, passing through the point (2,1).

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Chapter 16.1, Problem 42E

Chapter 16.1, Problem 44E

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An equation of the curve with the slope d y d x = y − x 3 y − x , passing through the point ( 2 , 1 ) .

Solution Summary: The author calculates an equation of the curve with the slope dy dx, passing through the point (2,1).

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To calculate: An equation of the curve with the slope dydx=y−x3y−x, passing through the point (2,1).

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Chapter 16 Solutions