Seatwork: Obtain the general solution of the following differential equations 1. (xy² + x) dx + (x²y - y) dy = 0 ans: (x²-1)(y² + 1) = c 2. dx = t (1 + t²) sec²x dt ans: 2x + sin2x = (1+ t²)² + c 3. y' y sec x = ans: y = c(sec x + tan x) 4. xv' (2v- 1) = v(x - 1) ans: x + 2y + c = In (xv)

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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Seatwork: Obtain the general solution of the following differential equations
1. (xy² + x) dx + (x²y - y) dy = 0
ans: (x²-1)(y² + 1) = c
2. dx = t (1 + t²) sec²x dt
ans: 2x + sin2x = (1+ ²)² + c
3. y' y sec x
ans: y = c(sec x + tan x)
4. xy' (2y - 1) = y (x - 1)
ans: x + 2y + c = In (xy)
5. x (y - 1) dx + (x + 1) dy = 0; if y = 2 when x = 1,
determine y when x = 2
ans: y = 1.55
6. sin x sin y dx +
cos x cos y dy = 0
7. sec 2x cos y dx
+ (cos 2x + cos 2x cot² y) dy = 0
ans: sin y = c cos x
ans: tan 2x + 2 In |csc y cot y = c
Transcribed Image Text:Seatwork: Obtain the general solution of the following differential equations 1. (xy² + x) dx + (x²y - y) dy = 0 ans: (x²-1)(y² + 1) = c 2. dx = t (1 + t²) sec²x dt ans: 2x + sin2x = (1+ ²)² + c 3. y' y sec x ans: y = c(sec x + tan x) 4. xy' (2y - 1) = y (x - 1) ans: x + 2y + c = In (xy) 5. x (y - 1) dx + (x + 1) dy = 0; if y = 2 when x = 1, determine y when x = 2 ans: y = 1.55 6. sin x sin y dx + cos x cos y dy = 0 7. sec 2x cos y dx + (cos 2x + cos 2x cot² y) dy = 0 ans: sin y = c cos x ans: tan 2x + 2 In |csc y cot y = c
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