Write the given nonlinear second-order differential equation as a plane autonomous system. x' = yl y' = X" + 7- 7x 1 + x² X 1 + x² 2 4y + 4x' = 0 Find all critical points of the resulting system. cx. n-( (00). (1,7) (x,
Write the given nonlinear second-order differential equation as a plane autonomous system. x' = yl y' = X" + 7- 7x 1 + x² X 1 + x² 2 4y + 4x' = 0 Find all critical points of the resulting system. cx. n-( (00). (1,7) (x,
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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
Transcribed Image Text:Write the given nonlinear second-order differential equation as a plane autonomous system.
x' = yl
y'
=
X
1 + x²
X" + 7-
7x
2
1 + x²
4y
+ 4x' = 0
Find all critical points of the resulting system.
cx. n)-( (0,0),(1,7)
(x, y)
=
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