O'zbekiston respublikasi oliy va o'rta maxsus talim vazirligi samarqand davlat universiteti haydarov Akram matematik fizika va analizning zamonaviy usullari va nokorrekt masalalari

A (jj-^ju = и'" + u' = /(x) |x| = 0 |x| > cost tenglama xususiy echimini toping

1. 
   u{x) = $*J1 - cos(x - y))f(y)dy
   
2. 
   u(x) = - cos(x - y))f(y)dy
   
3. 
   u(x) = /₀°°(1 - cos(x - y))f(y)dy
   

£"(x) - 3e'(x) + 2s(x) = 5(x) e(x) =?

1. 
   £(x) = в(х)(е^2х — e^x)
   
2. 
   £(x) = 6(x)(e^2x + e^x)
   
3. 
   £(x) = 6(x)e^2x
   
4. 
   £(x) = 6(x)e^x
   

и" — 3u' + 2и = f(x) tenglamaning xususiy echimini toping

1. 
   u(x) = f*Je²(^x-y) - e^x-y)f(y)dy
   
2. 
   u(x) = f₀^X(e²(^x~y) - e^x~y)f{y)dy
   
3. 
   u{x) = /"(e²^) - e^x-y)f(y)dy
   
4. 
   u{x) = $°_x{e²^ - e^x-y)f(y)dy
   

A(t) = 1, /₂(0 = t funksiyalar o'ramasini toping

a- fi*f₂=\t²

2. 
   /1 * /2 = t²
   
3. 
   /i*/₂ = l + t
   
4. 
   A*/₂ = (l + t)²
   
   121. 
        A(t) = 1, /2(0 — sint funksiyalar o'ramasini toping ^a- A * /2 = 1 — cost
        

b. /i*/₂ = l + t

100. 
     f_t*f₂ = cost
     
     4. 
        A*/₂ = (l + t)
        
        122. 
             f(t) = t² — 2t + l funksiyaning o'sish ko'rsatgichini toping a. (j — 0
             

b.	a =	1
c.	g =	2
d.	(j =	3
	/CO	—
a.	(J =	3
b.	g =	0
c.	(J =	l
d.	(J =	2
	/со	—
a.	(J =	0
b.	(J =	1
c.	g =	2
d.	(J =	3

125. 
     Integral tenglama yechimini toping /^c ch(t — r)x(r)dr = cht — cost
     
     1. 
        x(t) = Isint
        
     2. 
        x(t) = sint
        
     3. 
        x(t) = cost
        
     4. 
        x(t) = 2cost
        
126. 
     J^c sin(t — t) x(z)dz ning tasvirini toping
     
     1. 
        

s²+l ^{v y}

2. 
   — X(s)
   

s+1 ^{v J}

3. 
   

^{1 s} -ВД
s² +1

127. fсо s (t — t) x (t) dr о' ramaning tasvirini toping

f^£ '0

1. 
   

s²+l ^{v y}

2. 
   -^-ВД
   

s²+l ^{v y}

3. 
   ^-ВД
   

s²+1 ^{v y}

4. 
   -^-Д⁵)
   

s² + l ^{v J}
128. Integral tenglamani echimini toping С sh(t — т) x(r)dr = x(t) —
e"'

1. 
   x(t) = ch2t —-sh2t
   
2. 
   x(t) = ch2t
   
3. 
   x(t)=-sh2t
   

d. x(t) = shit 129. Integra - differensial tenglamani eching
e^{l T}sin(t — t) x(r)dr = x" — x' + e^z — e^zcost
о

1. 
   x(t) = t
   
2. 
   x(t) = 21
   
3. 
   x(t)=-t
   
4. 
   x(t) = t + 1
   

130. 
     Masalani xos funksiyasini toping X" + A²X = 0, Г(0) = 0, = 0
     
     1. 
        cos k = 0,1,2,...,
        

т->\ ■ ^k7T

2. 
   sin — x,
   

„s . 2fe+l

3. 
   sm. x,
   

' 21

4. 
   cos —j— x.
   
130. 
     Masalani xos qiymatlarini toping X" + Л²Х = 0, Г (0) = 0, X(l) = 0
     
     1. 
        A_fe=^TT, к = 0,1,2,...,
        
     2. 
        Л-fc - у.
        
131. 
     Masalani xoc funksiyasini toping X" + A²X = 0, *(0) = 0, X(f) = 0
     

A N . kn

1. 
   Sin — X, _ч kn
   
2. 
   COS-pX,
   
   100. 
        cos 7гх,
        

⁷ 2г
тлл • ^2k+1

4. 
   sm их.
   

' 21

133. 
     Masalani xos qiymatlarini toping X" + A²X = 0, *(0) = 0, X(£) = 0
     
     1. 
        A_fe=y, к = 1,2,3,...,
        
     2. 
        
        I
        ^{Як =} IP
        

134.To'lqin tenglamasi uchun aralash masalani echishda xos founksiyalarning qanday xossalaridan foydalaniladi

1. 
   ortogonallik xossasi
   
2. 
   maksimal qiymat prinsipining xossasidan
   
3. 
   maksimum qiymati prinsipi xassasidan
   
4. 
   Gyuygen prinsipidan 135.0'zgaruvchilarni ajratish usulining asoschisi kim
   
   1. 
      Fure,
      
   2. 
      Laplas,
      
   3. 
      Dalamber,
      
   4. 
      Gursa.
      
      136. 
           Bessel tenglamasini eching
           
           1.