[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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