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12. Find the family of solutions of the given differential equation and the family of orthogonal trajectories. Sketch both families. a. x dx + y dy = 0 b. x dy - 2y dx = 0

12. Find the family of solutions of the given differential equation and the family of orthogonal trajectories. Sketch both families. a. x dx + y dy = 0 b. x dy - 2y dx = 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In Exercises 5-10, find the orthogonal trajectories of the family of curves. Sketch several members of each family. 6. y = cx² 8. 2x² + y² = c² 9. y = ce * 10. y = ekx 11. Show that the curves 2x² + 3y² = 5 and y² = x³ are orthogonal. 12. Find the family of solutions of the given differential equation and the family of orthogonal trajectories. Sketch both families. a. x dx + y dy = 0 b. x dy – 2y dx = 0 5. y = mx 7. kx² + y² = 1
Transcribed Image Text:In Exercises 5-10, find the orthogonal trajectories of the family of curves. Sketch several members of each family. 6. y = cx² 8. 2x² + y² = c² 9. y = ce * 10. y = ekx 11. Show that the curves 2x² + 3y² = 5 and y² = x³ are orthogonal. 12. Find the family of solutions of the given differential equation and the family of orthogonal trajectories. Sketch both families. a. x dx + y dy = 0 b. x dy – 2y dx = 0 5. y = mx 7. kx² + y² = 1
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