Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Can you solve this question like another similar I added
![Solve the equation
(2х + 6) (2y? + 3) dx + 4y(x? + 3x + 2) dy %3D 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F335ab908-f55a-4dcd-94ac-3199a65caad5%2F1c475e48-413d-468d-afff-a9cb534bd593%2F57h5k0a_processed.png&w=3840&q=75)
Transcribed Image Text:Solve the equation
(2х + 6) (2y? + 3) dx + 4y(x? + 3x + 2) dy %3D 0
![Selns- Given equation is,
(or +4) Cy%, t) dx + (y (x43x + 9)) dy - o
-> Y(x?+3x +1) dy = - (x 4) ly*41) dx.
- (* +4) Cy"+1) dx.
y dy
y? + 1
X+4
x+ 3x+2
dx.
applying integhation an beth sides,
-> /, dy
X+4
-/-
x43x+2
multiphing 2
LY dy - -
beth Sides
=>
2 x + 8
x?+32+ 2
=>
2Y
dy
2X +3
y+1
7432+2
xp
x43x+2
t'cx)
In sC^)).
dx
(x)
-7
In Cy1) = -
A
B
- A(x+1) + B(x+1).
Ax+ 2A + Bx +B.
Compare * meiltiples bot sides,
A +B. -7 A = - B.
Conpore Constant teims both sices.
S : 2A +B.
-) - 2B + B
5.
=) A : 5,
5.
(x+1) (x+1)
In Cy?+1)
= cdn (x?+3x+2).
->
dx + /de.
Xナ」
-lo (x?+3X +2) - 5 In (x+1) + sIn (x +2).
ニ
- -dn (x?+3x+1) + s dn (*)
In (x²+3%+2) + in (
8+2
> in Cy41)
ニ
X+2
+3x+2
=) y4 1
(x + 2°
(x+1)5 ^ (x+1) (x+1).
yキ1.(ス+)
(x+2)1
(x +1) 6
1. -
is
the seperolte
(ox+2) 4
(x +1)8
:. Hence,
equation](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F335ab908-f55a-4dcd-94ac-3199a65caad5%2F1c475e48-413d-468d-afff-a9cb534bd593%2Fiakwhni_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Selns- Given equation is,
(or +4) Cy%, t) dx + (y (x43x + 9)) dy - o
-> Y(x?+3x +1) dy = - (x 4) ly*41) dx.
- (* +4) Cy"+1) dx.
y dy
y? + 1
X+4
x+ 3x+2
dx.
applying integhation an beth sides,
-> /, dy
X+4
-/-
x43x+2
multiphing 2
LY dy - -
beth Sides
=>
2 x + 8
x?+32+ 2
=>
2Y
dy
2X +3
y+1
7432+2
xp
x43x+2
t'cx)
In sC^)).
dx
(x)
-7
In Cy1) = -
A
B
- A(x+1) + B(x+1).
Ax+ 2A + Bx +B.
Compare * meiltiples bot sides,
A +B. -7 A = - B.
Conpore Constant teims both sices.
S : 2A +B.
-) - 2B + B
5.
=) A : 5,
5.
(x+1) (x+1)
In Cy?+1)
= cdn (x?+3x+2).
->
dx + /de.
Xナ」
-lo (x?+3X +2) - 5 In (x+1) + sIn (x +2).
ニ
- -dn (x?+3x+1) + s dn (*)
In (x²+3%+2) + in (
8+2
> in Cy41)
ニ
X+2
+3x+2
=) y4 1
(x + 2°
(x+1)5 ^ (x+1) (x+1).
yキ1.(ス+)
(x+2)1
(x +1) 6
1. -
is
the seperolte
(ox+2) 4
(x +1)8
:. Hence,
equation
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