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C. Family of Curves 1. Show that with distance from vertex to foci fixed as a, the family of curves solution of parabolas with axis parallel to the y-axis is 1 = = ±2ay". 2. Prove that when circles with center on the line y = -x and passing through the origin, it produces the solution (x² - 2xy - y²) dx + (x² + 2xy - y²) dy = 0.

C. Family of Curves 1. Show that with distance from vertex to foci fixed as a, the family of curves solution of parabolas with axis parallel to the y-axis is 1 = = ±2ay". 2. Prove that when circles with center on the line y = -x and passing through the origin, it produces the solution (x² - 2xy - y²) dx + (x² + 2xy - y²) dy = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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C. Family of Curves 1. Show that with distance from vertex to foci fixed as a, the family of curves solution of parabolas with axis parallel to the y-axis is 1 = +2ay". 2. Prove that when circles with center on the line y = -x and passing through the origin, it produces the solution (x² - 2xy − y²) dx + (x² + 2xy - y²) dy = 0.
Transcribed Image Text:C. Family of Curves 1. Show that with distance from vertex to foci fixed as a, the family of curves solution of parabolas with axis parallel to the y-axis is 1 = +2ay". 2. Prove that when circles with center on the line y = -x and passing through the origin, it produces the solution (x² - 2xy − y²) dx + (x² + 2xy - y²) dy = 0.
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