7-Mavzu: Mapleda differensial tenglamalarni yechish. Differensial tenglamalarni yechish funksiyalari. 1-, 2- va yuqori tartibli differensial tenglamalarni yechish

de:=diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=0;

2
4






 2
 

de:=

 4  2
 y( x)  y( x)  0
 x
y( x)
 x

• 
  dsolve(de, y(x), output=basis);
  cos(x), sin(x), x cos(x), x sin(x)
  Koshi masalasi yoki chegaraviy masalaning yechilishi.
  dsolve komanda Koshi masalasi yoki chegaraviy masalaning yechimini topishi mumkin, agarda berilgan differensial tenglama uchun noaniq funksiyaning boshlang’ich hamda chegaraviy shartlari berilsa. Boshlang’ich yoki chegaraviy shartlarda hosilalarni belgi-lash uchun differensial operator D ishlatiladi, masalan,
  

  y''(0)=2 shartni (D @@ 2)( y)(0)  2 kabi berishga to’g’ri keladi yoki y'(1)=0 shart-ni: Eslatib o’tamiz, n-chi tartibli hosila (D@@n)( y) kabi yoziladi. Koshi masalasining yechimini topish: y(4)+y''=2cosx, y(0)=2, y'(0)=1, y''(0)=0, y'''(0)=0.

Fan: Kompyuter algebrasi tizimlari O’qituvchi: T.Djiyanov II-kurs 7-Mavzu..

D( y)(1)  0 .

• 
  de:=diff(y(x),x$4)+diff(y(x),x$2)=2*cos(x);
  


 x2


 
   
 x4
 4  2
de : y( x)  y(x)  2 cos( x)

• 
  cond:=y(0)=-2, D(y)(0)=1, (D@@2)(y)(0)=0, (D@@3)(y)(0)=0;
  cond:=y(0)=2, D(y)(0)=1, (D(2))(y)(0)=0, (D(3))(y)(0)=0
  
• 
  dsolve({de,cond},y(x));
  y(x)=2cos(x)xsin(x)+x
  

 2 
 

Quyidagi chegaraviy masalaning yechimini topamiz: y'' y  2x   , y(0)  0 , y    0 . Yechim grafigini yasang.

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