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

 


 2  d3 
dx
3
y( x )
II-kurs
7-Mavzu..
Fan: Kompyuter algebrasi tizimlari O’qituvchi: T.Djiyanov
Ushbu ODEning yopiq shakldagi yechimlarini
mumkin.
topish uchun differensial Tenglamani differensial
Bu shuni ko'rsatadiki
(ko'paytuvchilarga ajratish yagona emas):

• right_fact := ode_fact[2];

homogeneous
Berilgan differensial tenglamaning har qanday yechimi tenglamaning yechimi bo'ladi. Bu quyidagi natijaga olib keladi:

• ode2 := diffop2de( right_fact, [DF,x], y(x) );

• dsolve( ode2, y(x) );

operatorlarining faktorizasiyasini ishlatish operatorga o'zgartirish mumkin:

• dode := de2diffop(ode,y(x), [DF,x]);

dode := x2 DF3  ( x3  x ) DF2  2 x2 DF  x3  x
va quyidagicha ko'paytuvchilarga ajratiladi:

• ode_fact := DFactor( dode, [DF,x] );




bitta faktorlash to'g'ri ko'paytuvchiga ega bo'ladi

ode_fact :=  x DF  x ( 2  x ), DF 
2 2 2
DF x2  1 
x 
x2

right_fact := DF 
2
DF x2  1
x
x2
ode2 := 
x2
d y( x )

x 



( x2  1 ) y( x ) dx  d2
dx
2
  y( x )
Fan: Kompyuter algebrasi tizimlari
O’qituvchi: T.Djiyanov
II-kurs
7-Mavzu..
Qolgan javoblar tartibni kamaytirish orqali yuqoridagi ikkita javobdan foydalangan holda aniqlanishi mumkin. Bu aslida dsolve da avval boshdagi ODEni yechish uchun qo'llanilgan metoddir:

• dsolve(ode);

y( x )  _C1 x BesselI( 0, x )  _C2 x BesselK( 0, x )



y( x )  _C1 x BesselI( 0, x )  _C2 x BesselK( 0, x )  _C3 x 
BesselI( 0, x ) 


 BesselK( 0, x ) e(  1/2 x2 )
x2
dx

 BesselI( 0, x ) e(  1/2 x2 )
x2

• BesselK( 0, x ) 



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