* Differentiate wo.r.t x. ↑ 介 x² + 5x²y² + y² = 2 =) 2x + 2x + (5x+1). 25 dy da + 1/[(522² +1) 8²] = 0 dy da dy da = ' (1/√6+1) (-2x-10xy) 2 (52+1).y (day) (√611) dy + y² [102] =0 @ da 10xy^) (x + 5xy") (5x + 1) y - ( √5 + 5/16) (5+1). for 6√6 11 (ii) differentiating again (*)
* Differentiate wo.r.t x. ↑ 介 x² + 5x²y² + y² = 2 =) 2x + 2x + (5x+1). 25 dy da + 1/[(522² +1) 8²] = 0 dy da dy da = ' (1/√6+1) (-2x-10xy) 2 (52+1).y (day) (√611) dy + y² [102] =0 @ da 10xy^) (x + 5xy") (5x + 1) y - ( √5 + 5/16) (5+1). for 6√6 11 (ii) differentiating again (*)
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
100%
can you please go over part 1 again as i still have no idea how you solved it espically the highligted parts, can you explain the questions and the answer more simply
![*
Differentiate wo.r.t x.
↑
介
x² + 5x²y² + y² = 2
=)
2x +
2x + (5x+1). 25
dy
da
+ 1/[(522² +1) 8²] = 0
dy
da
dy
da
=
' (1/√6+1)
(-2x-10xy)
2 (52+1).y
(day)
(√611)
dy + y² [102] =0 @
da
10xy^)
(x + 5xy")
(5x + 1) y
-
( √5 + 5/16)
(5+1).
for
6√6
11
(ii) differentiating again (*)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba7d748a-252c-474b-931e-93acb5db0c03%2F7b756908-7ca8-4923-8ed5-005bdfcd3d20%2F07vtveq_processed.png&w=3840&q=75)
Transcribed Image Text:*
Differentiate wo.r.t x.
↑
介
x² + 5x²y² + y² = 2
=)
2x +
2x + (5x+1). 25
dy
da
+ 1/[(522² +1) 8²] = 0
dy
da
dy
da
=
' (1/√6+1)
(-2x-10xy)
2 (52+1).y
(day)
(√611)
dy + y² [102] =0 @
da
10xy^)
(x + 5xy")
(5x + 1) y
-
( √5 + 5/16)
(5+1).
for
6√6
11
(ii) differentiating again (*)
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Follow-up Question
can you also go over part 2 again?
![d²y
S
2 + y(10x² + 2) days + dy se { dis 2 (1024+2) + y (202)})
dy
da
da
+ 10 [y² + 2xy day 2 ] = 0
dy
वधु
⇒2+y (102²+2) d² + (102²+2) (da) + 40xy da
da²
+ 10y² = 0
(1.²) to
=>2+ (10x + + 2) (14)
T
*222
=)2+
+ (10xㅎ +2)
(16²¹)
656
X 11
(22)+*+- 240 +10=6
(dy)
1x 23/1/1 x 017
(اره
22 (di bawa) (tor)
'd²y'
+ 10
11
6
36x6
11x11
36x36
-
=0
12x36_240 + 12 = 0](https://content.bartleby.com/qna-images/question/ba7d748a-252c-474b-931e-93acb5db0c03/76867920-2d45-4700-9732-ba68443d2aea/j348nl7_processed.png)
Transcribed Image Text:d²y
S
2 + y(10x² + 2) days + dy se { dis 2 (1024+2) + y (202)})
dy
da
da
+ 10 [y² + 2xy day 2 ] = 0
dy
वधु
⇒2+y (102²+2) d² + (102²+2) (da) + 40xy da
da²
+ 10y² = 0
(1.²) to
=>2+ (10x + + 2) (14)
T
*222
=)2+
+ (10xㅎ +2)
(16²¹)
656
X 11
(22)+*+- 240 +10=6
(dy)
1x 23/1/1 x 017
(اره
22 (di bawa) (tor)
'd²y'
+ 10
11
6
36x6
11x11
36x36
-
=0
12x36_240 + 12 = 0
Transcribed Image Text:Question 5
Suppose that y(x) is defined implicitly as a function of x by the following equa-
tion:
x² + 5x²y² + y² = 2
Note that (x, y) =(,1) satisfies this equation. Assume a > 0 and y > 0.
i. Find an expression for dy/dx and evaluate it at (,1).
ii. Find an expression for dy/da² and evaluate it at (,1).
iii. Find a second order Taylor approximation of y(x) about x =
√6
iv. Graph the approximating function you derived in iii.
Solution
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