) solve the ode: dx - (x + y + 1)dy = 0

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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2) solve the ode: dx - (x + y + 1)dy = 0
dy dt
Sol: let x + y + 1 = t, then 1+
dx
dx
dy dt
= then =
dx dx
1 then 1-t
tdt
dt
1-t+t=0 then (1 + t)dx + tdt = 0 then dx + = 0 dx +
dx
1 + t
dt
[ dx + √(1-₁1 4+4 +)
t/
then x + (x + y + 1) − ln(1 + x + y + 1) = c
then
dt
t(-1) = 0
dx
dt = c then x + t - ln(1 +t) = c
t + 1 - 1dt
1+t
Transcribed Image Text:2) solve the ode: dx - (x + y + 1)dy = 0 dy dt Sol: let x + y + 1 = t, then 1+ dx dx dy dt = then = dx dx 1 then 1-t tdt dt 1-t+t=0 then (1 + t)dx + tdt = 0 then dx + = 0 dx + dx 1 + t dt [ dx + √(1-₁1 4+4 +) t/ then x + (x + y + 1) − ln(1 + x + y + 1) = c then dt t(-1) = 0 dx dt = c then x + t - ln(1 +t) = c t + 1 - 1dt 1+t
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