4. For each of the following systems of differential equations, find the general solution and then sketch the phase portrait (i.e. graphs of solutions viewed in the phase plane) without using technology. -4x – 2y 4x + 2y dx 2x + y (b) (c) (a) -x - 3y x+3y x + y 4x - 2y (e) (f) !! (d) -4x -y 2x - y %3D -2x + y -3x - y 2x (g) (h) 6x+y 2y Il || I || Il I|

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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the phase portrait (i.e. graphs of solutions viewed in the phase plane) without using technology.
-4x – 2y
4. For each of the following systems of differential equations, find the general solution and then sketch
dx
4х + 2у
%3D
dx
dx
dt
dy
dt
(c) dy
2x + y
(b) dy
x + 3y
%3D
(a)
-3y
dt
||
x + y
dt
dx
dx
dt
(f) dy
%3D
dx
4х - 2у
(e)
dt
2x - y
-4x – Y
%3D
dt
dy
dt
(d)
dy
dt
dt
-2x + y
%3D
-3x - y
%3D
dx
dt
(g) dy
dt
(h) dy
2x
6x + y
%3D
2y
dt
dt
Transcribed Image Text:the phase portrait (i.e. graphs of solutions viewed in the phase plane) without using technology. -4x – 2y 4. For each of the following systems of differential equations, find the general solution and then sketch dx 4х + 2у %3D dx dx dt dy dt (c) dy 2x + y (b) dy x + 3y %3D (a) -3y dt || x + y dt dx dx dt (f) dy %3D dx 4х - 2у (e) dt 2x - y -4x – Y %3D dt dy dt (d) dy dt dt -2x + y %3D -3x - y %3D dx dt (g) dy dt (h) dy 2x 6x + y %3D 2y dt dt
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