Let y(x) = cx³ be a one-parameter family of cubic polynomials.(a) Show that the family of curves that is orthogonal at every point of the (x, y)-plane to this family of cubics satisfiesthe following differential equation.X3yThe slope y'(x) = m =of functions must satisfy the differential equation y'y. Using c = gives m =x3Using implicit differentiation on x² + 3y² = C givesequation for y' gives y' ==(b) Show that the set of curves x² + 3y² = C is a one-parameter family satisfying the differential equation y'part (a).X1Зу'VX3yas desired.+(c) Either using a curve-plotting program, or by hand, sketch the curves y =x² + 3y² = C for C = 1, 2, 3.Therefore, the orthogonal familycx³ for c =X3yVy' = 0. Solving this±1, c = ±2 and the curvesin

Since you have posted a multiple question according to guidelines I will solve first(a) question…

Answered: Let y(x) = cx³ be a one-parameter…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.CR: Chapter 9 Review

Problem 54CR

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