Match the direction field with systems of differential equation (a)(c)(e)(b)(d)(f)-1(i)(iv)(vii)dxx² – 1dtdxdx(x + 1)(y² – 1)dt-x2 + 2x – 1dtdydy= y² – 1dt= x² – 2x + 1dtdyy? – 1dt(ii)(v)(viii)dx= (x – 1)(y – 1)dxdx(1 – x)(y + 1)dt= -y² + 2y – 1dtdtdy(x + 1)(y+ 1)dtdydy(x+ 1)(y – 1)dt= y? + 2y + 1dt(iii)(vi)(ix)dxdxdx= (2² – 1)(y – 1)dt–x² + 2x – 1-x? – 2x – 1dtdtdydydy-x² – 2x –-y? + 1dt-y – 11dtdt||||||||

Answered: Image /qna-images/answer/d9715822-5ab4-4077-9a56-5b840e949ac3.jpg

(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

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Match the direction field with systems of differential equation

(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
||
||
||
||

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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