Explanation Procedure used: Figure below shows the reflecting surface. Figure-(1) Consider the angle of incidence equal to the angle of reflection to determine the differential equation that describes the shape of the curve. Calculation: The value of angle between P M and O M is, tan ( π − ϕ ) = P M O M − tan ϕ = − y x tan ϕ = y x (1) Sum of internal angles of the triangle P N O is same as an external angle at O as the angle of incidence equal to the angle of reflection. 2 θ = ϕ tan 2 θ = tan ϕ tan 2 θ = y x 2 tan θ 1 − tan 2 θ = y x (2) The value of slope of tangent at P is, y ′ = tan θ Substitute y ′ for tan θ in equation (2). 2 y ′ 1 − y ′ 2 = y x 2 x y ′ = y − y y ′ 2 y y ′ 2 + 2 x y ′ − y = 0 (3) Solve quadratic equation (3)

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 1.3, Problem 29E

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The differential equation that describes the shape of the curve.

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Chapter 1.3, Problem 28E

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