Given the following linear system of ODE: V₁' = 4y1+2V2 V₂' = 10/1-4/2 what is the type of the critical point? the critical point is improper node the critical point is center the critical point is spiral the critical point is saddle the critical point is proper node

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Given the following linear system of ODE:
V₁' = 4y1+2V₂
V₂' = 10/1-4/2
what is the type of the critical point?
the critical point is improper node
the critical point is center
the critical point is spiral
O the critical point is saddle
the critical point is proper node
Transcribed Image Text:Given the following linear system of ODE: V₁' = 4y1+2V₂ V₂' = 10/1-4/2 what is the type of the critical point? the critical point is improper node the critical point is center the critical point is spiral O the critical point is saddle the critical point is proper node
Given ODE as following:
xy" + xy' - 4y = x
2.
what is the general solution?
-2
y=C₁x² + ₂x² + C3x-3
-3
-2
y=x² + x²+x=³
Ov=C₁x² + ₂x-²
Oy=c₁x² + C₂x¯²+3x¯5
-2
OV=C₁x² + ₂x² +0.2x-³
Transcribed Image Text:Given ODE as following: xy" + xy' - 4y = x 2. what is the general solution? -2 y=C₁x² + ₂x² + C3x-3 -3 -2 y=x² + x²+x=³ Ov=C₁x² + ₂x-² Oy=c₁x² + C₂x¯²+3x¯5 -2 OV=C₁x² + ₂x² +0.2x-³
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