(i) Solve the linear system below using Laplace Transforms dx dt for some real constant a, and X(o) = 0, y (0) = 1 =-ax+y, dy dt =X-ay (ii) Find the range of values of a where (X, Y)-(0,0) is an unstable saddle. (iii) If a = 0.1, what initial conditions x(0) >xo, y(0) > yo near (x,y) will guarantee a faster rate of consumer uptake of electric cars than conventional cars? [Hint: Plot the phase portrait!]
(i) Solve the linear system below using Laplace Transforms dx dt for some real constant a, and X(o) = 0, y (0) = 1 =-ax+y, dy dt =X-ay (ii) Find the range of values of a where (X, Y)-(0,0) is an unstable saddle. (iii) If a = 0.1, what initial conditions x(0) >xo, y(0) > yo near (x,y) will guarantee a faster rate of consumer uptake of electric cars than conventional cars? [Hint: Plot the phase portrait!]
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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![(i) Solve the linear system below using Laplace Transforms
dx
dt
-=-ax+y, dy
dt
for some real constant a, and X(o) = 0, y (0) = 1
J
=X-ay
=
(ii) Find the range of values of a where (X, Y)-(0,0) is an unstable saddle.
(iii) If a = 0.1, what initial conditions x(0) >xo, y(0) > yo near (x...) will guarantee a faster rate of consumer
uptake of electric cars than conventional cars? [Hint: Plot the phase portrait!]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12fdac56-4b52-4434-8b00-5772085cd8ad%2F1d79826a-7671-44a5-afb3-089f211bb277%2F1n8enn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(i) Solve the linear system below using Laplace Transforms
dx
dt
-=-ax+y, dy
dt
for some real constant a, and X(o) = 0, y (0) = 1
J
=X-ay
=
(ii) Find the range of values of a where (X, Y)-(0,0) is an unstable saddle.
(iii) If a = 0.1, what initial conditions x(0) >xo, y(0) > yo near (x...) will guarantee a faster rate of consumer
uptake of electric cars than conventional cars? [Hint: Plot the phase portrait!]
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