O'zbekiston respublikasi oliy va o'rta maxsus talim vazirligi samarqand davlat universiteti haydarov Akram matematik fizika va analizning zamonaviy usullari va nokorrekt masalalari
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- y))f(y)dy
- ch(t — r)x(r)dr = cht — cost
- t) x(r)dr =
- X" + A
A (jj-^ju = и'" + u' = /(x) |x| = 0 |x| > cost tenglama xususiy echimini toping
u{x) = $*J1 - cos(x - y))f(y)dy u(x) = - cos(x - y))f(y)dy u(x) = /0°°(1 - cos(x - y))f(y)dy £"(x) - 3e'(x) + 2s(x) = 5(x) e(x) =? £(x) = в(х)(е2х — ex) £(x) = 6(x)(e2x + ex) £(x) = 6(x)e2x £(x) = 6(x)ex и" — 3u' + 2и = f(x) tenglamaning xususiy echimini toping u(x) = f*Je2(x-y) - ex-y)f(y)dy u(x) = f0X(e2(x~y) - ex~y)f{y)dy u{x) = /"(e2^) - ex-y)f(y)dy u{x) = $°x{e2^ - ex-y)f(y)dy A(t) = 1, /2(0 = t funksiyalar o'ramasini toping a- fi*f2=\t2 /1 * /2 = t2 /i*/2 = l + t A*/2 = (l + t)2 A(t) = 1, /2(0 — sint funksiyalar o'ramasini toping a- A * /2 = 1 — cost b. /i*/2 = l + t ft*f2 = cost A*/2 = (l + t) f(t) = t2 — 2t + l funksiyaning o'sish ko'rsatgichini toping a. (j — 0
Integral tenglama yechimini toping /c ch(t — r)x(r)dr = cht — cost x(t) = Isint x(t) = sint x(t) = cost x(t) = 2cost Jc sin(t — t) x(z)dz ning tasvirini toping s2+l v y — X(s) s+1 v J 1 s -ВД s2 +1 127. fсо s (t — t) x (t) dr о' ramaning tasvirini toping f£ '0 s2+l v y -^-ВД s2+l v y ^-ВД s2+1 v y -^-Д5) s2 + l v J 128. Integral tenglamani echimini toping С sh(t — т) x(r)dr = x(t) — e"' x(t) = ch2t —-sh2t x(t) = ch2t x(t)=-sh2t d. x(t) = shit 129. Integra - differensial tenglamani eching el Tsin(t — t) x(r)dr = x" — x' + ez — ezcost о x(t) = t x(t) = 21 x(t)=-t x(t) = t + 1 Masalani xos funksiyasini toping X" + A2X = 0, Г(0) = 0, = 0 cos k = 0,1,2,..., т->\ ■ k7T sin — x, „s . 2fe+l sm. x, ' 21 cos —j— x. Masalani xos qiymatlarini toping X" + Л2Х = 0, Г (0) = 0, X(l) = 0 Afe=^TT, к = 0,1,2,..., Л-fc - у. Masalani xoc funksiyasini toping X" + A2X = 0, *(0) = 0, X(f) = 0 A N . kn Sin — X, ч kn COS-pX, cos 7гх, 7 2г тлл • 2k+1 sm их. ' 21 Masalani xos qiymatlarini toping X" + A2X = 0, *(0) = 0, X(£) = 0 Afe=y, к = 1,2,3,..., I Як = IP 134.To'lqin tenglamasi uchun aralash masalani echishda xos founksiyalarning qanday xossalaridan foydalaniladi ortogonallik xossasi maksimal qiymat prinsipining xossasidan maksimum qiymati prinsipi xassasidan Gyuygen prinsipidan 135.0'zgaruvchilarni ajratish usulining asoschisi kim Fure, Laplas, Dalamber, Gursa. Bessel tenglamasini eching Download 391.68 Kb. Do'stlaringiz bilan baham: |
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