[a] z = dz dr D 4+4-³ P d/y +2 = (4+48-8³) a (x³/2) - 83/2 d (4+48 -√3) (4+48-83)2 3 (4+48-8³) 50 - 8³/2 (4-38²) (4+ 4r-x3² = 65 + 6×5² - 2² x³√x - (4+4r-r3)2 = √r (6+2× +38²³) (4+48-√3)² = √r (12+ 4r +38³) 2(4+48-8³)2 42√5 + 38³√r [b] w= dw = du 44+1 4 ³4 (012) (4011) - (AU11) { 2 ³/4 + {²} 42 (U12)² 24² - 3u u²4 { 4 (²+2) - (U+1) (qu}} ₂ (0+2) 2 40²484-94²-104 -24-2 14 (4+2)² - [ 6u³+1 24² - 3 (2441) + 20u²+ 17u + 10 4u²4 (4+2)² [c] f(x) = f'(x) = (x²-x+1) (0) - 1(2x-1) f"(x) = (x²-x11) ² (-2)-(1-2x) (2) (x²-11) (2x-1) (x²-x+1)+ - 2x²+2x-2 +2 (4x²+1-4x) (x²-x^2) f(¹) = 1-2x (x²-x71)² F 6x² - 6x (x²-x+1)* (x²³=x+1)+ (12x-6) (6x²64) (x²-x+1)³(2x-1) f"(x) = f" (1) = ₁^ (6) - (0x4) (1) (1) 1 6
[a] z = dz dr D 4+4-³ P d/y +2 = (4+48-8³) a (x³/2) - 83/2 d (4+48 -√3) (4+48-83)2 3 (4+48-8³) 50 - 8³/2 (4-38²) (4+ 4r-x3² = 65 + 6×5² - 2² x³√x - (4+4r-r3)2 = √r (6+2× +38²³) (4+48-√3)² = √r (12+ 4r +38³) 2(4+48-8³)2 42√5 + 38³√r [b] w= dw = du 44+1 4 ³4 (012) (4011) - (AU11) { 2 ³/4 + {²} 42 (U12)² 24² - 3u u²4 { 4 (²+2) - (U+1) (qu}} ₂ (0+2) 2 40²484-94²-104 -24-2 14 (4+2)² - [ 6u³+1 24² - 3 (2441) + 20u²+ 17u + 10 4u²4 (4+2)² [c] f(x) = f'(x) = (x²-x+1) (0) - 1(2x-1) f"(x) = (x²-x11) ² (-2)-(1-2x) (2) (x²-11) (2x-1) (x²-x+1)+ - 2x²+2x-2 +2 (4x²+1-4x) (x²-x^2) f(¹) = 1-2x (x²-x71)² F 6x² - 6x (x²-x+1)* (x²³=x+1)+ (12x-6) (6x²64) (x²-x+1)³(2x-1) f"(x) = f" (1) = ₁^ (6) - (0x4) (1) (1) 1 6
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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Question
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TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT
![[9] z =
11
[1
11
312
=
4+48
312
dz- & (2²) + df (2)
=
dr
dr
-
83
+2
(4+48-8³) a (x²³/2) - 8³/2 d (4+48 -√³)
dr
(4+48-83)²
3 (4+40-23) Jo
2
-
65 +6r5
(4+42-83)²
3
2
350
= √r (6+27 +22³)
2
(4+48-8¹) ²
23/2 (4-38²)
(4+48-8³)²
√5 (12+ 48 +38³)
2 (4+48-√³)2
42√5 + 38³√r
[b] w=
dw
du
=
15
JJ
4u+1
u514 (U+2)
3
24
5/4 (U+2) d (4u+1) - (Aut 1) { u
u
45/12 (4+2)²
3
242
- [
44² +84-94²- 10u
²³/4 (4+2)²
и
6u³+1
24²
-342
3u
u²4 { 4 (u²+₂u) - (Au+1) { 2 u + 2 } }
45/2 (4+2) ²
+
514
- 12/24 - 12/20
들
- {U²4 }
2042²+ 174 + 10
4u²4 (4+2)²
t
जान
-3 -34
24²
3 (24³+1)
24.²
[c] f(x) =
f'(x) =
f'(x)
f"(x)
f"" (1)
19
=
x
1
X+ I
(x²-x + ₁) ( 0) − 1 (2x-1)
-
(x²-x(+1)
1-2x
(x²-x + 1)²
2
6x²
(x²-x+1)² (-2) - (1-2x) (2) (x²-x+1) (2x-1)
(x²-x+1)+
- 2x²+2x-2 +2 ( 4x²+1-4x)
(x²-x+1)+
f" (1) = √6)
-
2
2
(x²-x+1)*
3
f"(x) = (x ²³= x + 1) + (12x-6) - (6x²6x) (4) (x²-x+1)³² (2x-1)
(x²-x+1)
(0x4) (1) (1)
1^ (6)
6x
2
1
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4be50db6-19e4-41fe-8b0c-6d619944736f%2F47bfd482-2377-485a-af73-986c1bcd0509%2Fqa708n7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[9] z =
11
[1
11
312
=
4+48
312
dz- & (2²) + df (2)
=
dr
dr
-
83
+2
(4+48-8³) a (x²³/2) - 8³/2 d (4+48 -√³)
dr
(4+48-83)²
3 (4+40-23) Jo
2
-
65 +6r5
(4+42-83)²
3
2
350
= √r (6+27 +22³)
2
(4+48-8¹) ²
23/2 (4-38²)
(4+48-8³)²
√5 (12+ 48 +38³)
2 (4+48-√³)2
42√5 + 38³√r
[b] w=
dw
du
=
15
JJ
4u+1
u514 (U+2)
3
24
5/4 (U+2) d (4u+1) - (Aut 1) { u
u
45/12 (4+2)²
3
242
- [
44² +84-94²- 10u
²³/4 (4+2)²
и
6u³+1
24²
-342
3u
u²4 { 4 (u²+₂u) - (Au+1) { 2 u + 2 } }
45/2 (4+2) ²
+
514
- 12/24 - 12/20
들
- {U²4 }
2042²+ 174 + 10
4u²4 (4+2)²
t
जान
-3 -34
24²
3 (24³+1)
24.²
[c] f(x) =
f'(x) =
f'(x)
f"(x)
f"" (1)
19
=
x
1
X+ I
(x²-x + ₁) ( 0) − 1 (2x-1)
-
(x²-x(+1)
1-2x
(x²-x + 1)²
2
6x²
(x²-x+1)² (-2) - (1-2x) (2) (x²-x+1) (2x-1)
(x²-x+1)+
- 2x²+2x-2 +2 ( 4x²+1-4x)
(x²-x+1)+
f" (1) = √6)
-
2
2
(x²-x+1)*
3
f"(x) = (x ²³= x + 1) + (12x-6) - (6x²6x) (4) (x²-x+1)³² (2x-1)
(x²-x+1)
(0x4) (1) (1)
1^ (6)
6x
2
1
1
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