Explanation Given: The given differential equation is, y [ 1 + ( y ′ ) 2 ] = k And the given equation to be used for substitution is, y = k sin 2 θ (1) Calculation: Solve the given differential equation for d x in terms of y and d y . [ 1 + ( d y d x ) 2 ] = k y ( d y d x ) 2 = k y − 1 d y d x = k y − 1 d y k y − 1 = d x (2) Differentiate equation (1) with respect to d θ . d y = 2 k sin θ cos θ d θ (3) Substitute the value of d y from equation (3) and value of y from equation (1) in equation (2) and then integrate the equation on both sides

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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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 2, Problem 38CR

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The solution of the given differential equation using appropriate substitution method to obtain a parametric form of solution.

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Chapter 2, Problem 37CR

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The solution of the given differential equation using appropriate substitution method to obtain a parametric form of solution.

Solution Summary: The author explains the parametric solution of the given differential equation using appropriate substitution method.

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The solution of the given differential equation using appropriate substitution method to obtain a parametric form of solution.

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Chapter 2 Solutions