1. Use the integrating factor method to solve the following ODES. (a) (b) (c) SE SE SES dy dt dy 2 dt - 3t²y = 4tet³, y(0) = 1 2t+5, y(1) = 1 du + -y ty dy 3y dt t + = t², y(2) = 1

Calculus: Early Transcendentals
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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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1. Use the integrating factor method to solve the following ODES.
dy
dt
3t²y = 4tet³, y(0) = 1
dy
2
(b) + −y= 2t+5, y(1) = 1
dt
(a)
dy 3y
(c) + t², y(2) = 1
dt t
dy
(d) +3t²y = 6t², y(0) = 7
dt
2. For the following ODEs: (i) find equilibrium points, (ii) make a phase line to determine
if the points are stable or unstable, and (iii) draw a trajectory plot.
(a)
(b)
(c)
dy 2
dt
dy
dt
dy
dt
= y² – 1
=
y - y³
3
= y² + 5y − 14
-
Transcribed Image Text:1. Use the integrating factor method to solve the following ODES. dy dt 3t²y = 4tet³, y(0) = 1 dy 2 (b) + −y= 2t+5, y(1) = 1 dt (a) dy 3y (c) + t², y(2) = 1 dt t dy (d) +3t²y = 6t², y(0) = 7 dt 2. For the following ODEs: (i) find equilibrium points, (ii) make a phase line to determine if the points are stable or unstable, and (iii) draw a trajectory plot. (a) (b) (c) dy 2 dt dy dt dy dt = y² – 1 = y - y³ 3 = y² + 5y − 14 -
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