we have to two h(x) = n'(x) = of the function h(x) = h₁(x) = h(x) 1(x) x² √5-3x 11 11 find. = the derivative of order 2 7² 5-3x 1 Differentiating get. √5-3x · Qx - x²-½ (5-3x)²¯.! (-3) (√5-3x.) ² √5-3x 2x + Again differentiating h" (x) = (5-3x) 2.2x (5-3x) + 3x² (5-3x). √5-3x 20x12x² + 3x² (5-3x) 2 20x-9x² (5-3x) 3x2² √√5-3x 2 we get. (5-3x) * (20-18z) – (20x-9x²). 2- (5-3x) = (-3) ((5-32.) ³2) ² we (5-3x)² (20-18x) + 2 (20-9ײ¹) (5-3x) ¹² (5-3x)³ (5-3x) ¹2 (5-3x) (20-18x) + 2/2 (20-9x² (5-3x)² 2 (5-3x)²² 2100-60x-90x + 51x² + ² (20-9x²) } (5-3x.) ³ (5-3x) ²20 200 - 300x + 108 x ² + 180-81x²} 2 (5-3x) 27x²-300x+380 2 (5-3x) = 1/2
we have to two h(x) = n'(x) = of the function h(x) = h₁(x) = h(x) 1(x) x² √5-3x 11 11 find. = the derivative of order 2 7² 5-3x 1 Differentiating get. √5-3x · Qx - x²-½ (5-3x)²¯.! (-3) (√5-3x.) ² √5-3x 2x + Again differentiating h" (x) = (5-3x) 2.2x (5-3x) + 3x² (5-3x). √5-3x 20x12x² + 3x² (5-3x) 2 20x-9x² (5-3x) 3x2² √√5-3x 2 we get. (5-3x) * (20-18z) – (20x-9x²). 2- (5-3x) = (-3) ((5-32.) ³2) ² we (5-3x)² (20-18x) + 2 (20-9ײ¹) (5-3x) ¹² (5-3x)³ (5-3x) ¹2 (5-3x) (20-18x) + 2/2 (20-9x² (5-3x)² 2 (5-3x)²² 2100-60x-90x + 51x² + ² (20-9x²) } (5-3x.) ³ (5-3x) ²20 200 - 300x + 108 x ² + 180-81x²} 2 (5-3x) 27x²-300x+380 2 (5-3x) = 1/2
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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Transcribed Image Text:we have to
two
h(x) =
n'(x)
h₁(x)
of
1 (x²)
L" (x)
x²
√5-3x
11
find
=
the function h(x) =
the derivative of order
Differentiating we
√5-3x-2x - x
(√5-3K.)²
Again differentiating
h"(x)
√√5-3x2x +
x² / (5-3x)² = (-3)
(5-3x)
2.2x (5-3x) + 3x²
(5-3x). √5-3x
20x12x² + 3x²
(5-3x) ²2/2
20x-9x²
(5-3x)
3x²
2
we
2
√5-3x
(5-3x) ² (100-60x
x
√5-3x
get.
(5-3x)² (20- 18x) – (20x-9x²). —— (5-3x)² (65)
2
(5-3x)²³2) ²
get.
27x²-300x + 380
2 (5-3x) 51/2
²
(5-3x)² (20-18x) + 2/2 (20-9x²) (5-3x)
(5-3x.)³
(5-3x) ¹2 (5-3x) (20-18x) + 2/2 (20-9x²)}
(5-3x)²
60x-90x + 51x² + ²/2 (20-9x²) }
3
(5-3x.) ³
(5-3x) = {2 200 - 300x + 108x² +180 - 812²}
2 (5-3x)²³
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