Answered: find a set of solutions unless the…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter13: Conic Sections

Section13.1: Circles

Problem 48PS

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I. In each exercise, find a set of solutions unless the statement of the exercise stipulates otherwise. Use any method. 1. (3xy + 3y — 4)dx + (x + 1) 2 dy = 0 2. (x + y) dx + x dy = 0 3. y 2dx — x(2x + 3y)dy = 0 4. (x 2 + l)dx + x 2 y 2dy = 0 5. y ′ = x 3 — 2xy; when x = 1; y = 2 6. sinθ dr dθ = —1 — 2r cosθ 7. dx dt = cosx cos2 t 8. y(x + 3y) dx + x 2 dy = 0 9. 3x 3 y′ = 2y(y — 3). 10.dy dx = sec2 x sec3 y 11.xy(dx — dy) = x 2 dy + y 2 dx 12.(y — sin2 x) dx + sin x dy = 0 13.(y 2 − 3y − x) dx + (2y − 3) dy = 0 14.(y 3 + y + 1)dx + x(x − 3y 2 − 1)dy = 0 15.(x + 3y − 5)dx − (x − y − 1) dy = 0 16.(x 5 — y 2 )dx + 2xy dy = 0 17.(2x + y — 4)dx + (x − 3y + 12)dy = 0 18.(y 3 sec2 xdx − (1 — 2y 2 tanx)dy = 0 19.x 3 ydx + (3x 4 — y 3 )dy = 0 20.dy/dx = tan y cot x — sec y cosx 21.(6xy — 3y 2 + 2y) dx + 2(x − y) dy = 0 22.(x —2) dx + 4(x + y— 1) dy = 0 23.(sin y — y sin x)dx + (cosx + x cos y)dy = 0 24.(1 + 4xy — 4x 2y)dx + (x 2 — x 3 )dy = 0; when x = 2, y = 1 4 25.(2y cosx + sin4 x)dx = sin x dy , when x = π 2 , y = 1

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