Find (u, v), u, v|, and d(u, v) for the given inner product definu-(-5,4), v = (0,-2), (u, v) = 3u v + uzsn) (e)(u, v)(b)V 41(c)2.(d)(^'n)pV61

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Answered: Find (u, v), u, v|, and d(u, v) for the…

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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(x2y-)水 + (2x +y+) dy~ 0 let メーuー1, dx = du yov-l, dy ody LINE 1 %3D LINE 2 (4-1+ 2y - 2-1) du t (2u-2+ v -I+1) dy =0 (u+ 2x) du + (2u + v) dy レINE 3 LINE 4 ミO let u= 2y du こ 2dy + yd2 レINE S LINE 6 (ZY + 2Y)(zdvt ydz) + (22y +y)dx =0 LINE 8 (2+2)( zdv + vdz) + (22 t1) dy = 0 LINE 7 ○=Xp(人+人そ2 LINE 9 (22+ 2え)d +(22+1)d+ (2+2) vd2= 0 Qコ入や(1+ぞて +P^(て+そ) + Pモ (て十そ) LINE 10 %3D (2²+ 27 t 1) av + (2+2)ydz =0 2+2-dz 22+42 + In (x) + Y2 In (22t 42+1) = C LIANE 14 In (vZ) + In (2²+ 4z+) =C In Lv (22 +42 +1]-'C LINE II LINE 12 LINE 13 LINE IS LINE Ib ye (z-+42+)こC v2 (Wん + 4u +)=C u2 + 4uy t yZ LINE 7 LINE 18 LINE 19 v( 42 + 4uY+x2=C (メ)2+4[xtり(リー)+ (yー)2-C レINE 20 LINE 21 %3D
Orthogonalize {1, t, t²} in P₂ (R) with 2 1 (f,g) = [*, f(x)g(x) dx. -1 Then normalize each one so that its graph passes through (1,1). These are the first three Legendre polynomials. " " 2 }
only b
Given f(x, y, z) = x5yz², find a2f and f₂(1, 1, 1). ахду a2f дуду f₂(1, 1, 1) =
The differential eauation, こD (メナ3y-5)メ- (3x+yーラ)dy Can be transfor med Into homogeneous differential eguation ,only afer using the substitution equations y=y' tk and x =x' th . Determine Chik). A) (1,2) B.) (2,1) c) (1,-2) D) (-2い)
Compute the following linear combinations for u = (1, 2), v = (4, -1), and w = (-1, 3). (a) u + w (b) u + 3v (c) v + w (d) 2u + 3v - w (е) —Зи + 4v — 2w
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Find (u, v), u, v|, and d(u, v) for the given inner product defin u-(-5,4), v = (0,-2), (u, v) = 3u v + uzs (-5, 4), (a) (u, -8 (b) V41 (c) 2. (d) (^'n)p V61