Explanation Calculation: To convert the given equation into polar coordinates, Let x = r cos θ and y = r sin θ , Apply product rule in the both equation above, d x = cos θ d r − r sin θ d θ d y = sin θ d r + r cos θ d θ Substitute the values in the given differential; equation. sin θ d r + r cos θ d θ cos θ d r − r sin θ d θ = 4 ( r cos θ ) + ( r sin θ ) ( r cos θ ) − 4 ( r sin θ ) sin θ d r + r cos θ d θ cos θ d r − r sin θ d θ = 4 cos θ + sin θ cos θ − 4 sin θ sin θ d r + r cos θ d θ ( cos θ − 4 sin θ ) = cos θ d r − r sin θ d θ ( 4 cos θ + sin θ ) [ sin θ d r ( cos θ ) − sin θ d r ( 4 sin θ ) + r cos θ d θ ( cos θ ) − r cos θ d θ ( 4 sin θ ) ] = [ cos θ d r ( 4 cos θ ) + cos θ d r ( sin θ ) − r sin θ d θ ( 4 cos θ ) − r sin θ d θ ( sin θ ) ] Further simplify as, [ sin θ cos θ d θ − 4 sin 2 θ d r + r cos 2 θ d θ − r 4 sin θ cos θ d θ ] = [ 4 cos 2 θ d θ + sin θ cos θ d r − r 4 sin θ cos θ d θ − r sin 2 θ d θ ] [ − 4 sin 2 θ d r + r

Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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Differential Equations

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 1.8, Problem 24P

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The differential equation dydx=4x+yx−4y by first transforming it into polar coordinates.

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Chapter 1.8, Problem 23P

Chapter 1.8, Problem 25P

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The differential equation d y d x = 4 x + y x − 4 y by first transforming it into polar coordinates.

Solution Summary: The author explains how to solve the differential equation by first transforming it into polar coordinates.

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To solve:

The differential equation dydx=4x+yx−4y by first transforming it into polar coordinates.

Want to see the full answer?

Chapter 1 Solutions

The differential equation d y d x = 4 x + y x − 4 y by first transforming it into polar coordinates.

Solution Summary: The author explains how to solve the differential equation by first transforming it into polar coordinates.

Concept explainers

Videos

To solve: The differential equation dydx=4x+yx−4y by first transforming it into polar coordinates.

Want to see the full answer?

Chapter 1 Solutions

To solve:

The differential equation dydx=4x+yx−4y by first transforming it into polar coordinates.