(i) (iv) (vii) dx x2 dx = (x + 1)(y² – 1) dx 1 –x² + 2x – 1 %3D = - | dt dt dt dy dy dy = x² – 2x + 1 dt 1 - 1 %3D | dt dt (ii) (v) (viii) dx = (x – 1)(y – 1) dx dx = (1 – x)(y+1) -y? + 2y – 1 dt dt dt dy = (x + 1)(4 +1) dy = (x +1)(y – 1) dy = y + 2y +1
(i) (iv) (vii) dx x2 dx = (x + 1)(y² – 1) dx 1 –x² + 2x – 1 %3D = - | dt dt dt dy dy dy = x² – 2x + 1 dt 1 - 1 %3D | dt dt (ii) (v) (viii) dx = (x – 1)(y – 1) dx dx = (1 – x)(y+1) -y? + 2y – 1 dt dt dt dy = (x + 1)(4 +1) dy = (x +1)(y – 1) dy = y + 2y +1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Match the direction field with systems of
Transcribed Image Text:(a)
(c)
(e)
(b)
(d)
(f)
-1
(i)
(iv)
(vii)
dx
x² – 1
dt
dx
dx
(x + 1)(y² – 1)
dt
-x2 + 2x – 1
dt
dy
dy
= y² – 1
dt
= x² – 2x + 1
dt
dy
y? – 1
dt
(ii)
(v)
(viii)
dx
= (x – 1)(y – 1)
dx
dx
(1 – x)(y + 1)
dt
= -y² + 2y – 1
dt
dt
dy
(x + 1)(y+ 1)
dt
dy
dy
(x+ 1)(y – 1)
dt
= y? + 2y + 1
dt
(iii)
(vi)
(ix)
dx
dx
dx
= (2² – 1)(y – 1)
dt
–x² + 2x – 1
-x? – 2x – 1
dt
dt
dy
dy
dy
-x² – 2x –
-y? + 1
dt
-y – 1
1
dt
dt
||
||
||
||
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