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

Biz bu operatorlari ko'paytirib shuni eslatib o'tishimiz mumkinki, ularni o'rnini almashtirib bo'lmaydi: L4 := collect( mult( L1, L2, [DF, x] ), DF );

Fan: Kompyuter algebrasi tizimlari O’qituvchi: T.Djiyanov II-kurs 7-Mavzu..
Argument [DF, x] mult komandasiga ko'paytirish DF va x belgilab bergan differensial sohasi ustida ekanligini ko'rsatadi, shuning uchun a va b o'zgaruvchilari o'zgarmas songa teng. Bu yana _Envdiffopdomain := [DF, x], muhit o'zrgaruvchisi orqali belgilanishi mumkin.
Bir tomonli eng kichik umumiy ko'paytuvchi va eng katta umumiy bo'luvchi tushunchasi shunday sohalarda mavjud bo'ladi. Misol tariqasida,

• L6 := LCLM( L3, L2, [DF, x] );

L4 := x3 DF3  ( x4  x2  x2 b ) DF2  ( a x  x b  x  4 x3 ) DF  a x2  x4  x2 b  a b

• L5 := collect( mult( L2, L1, [DF, x] ), DF );

L5 :=
x3 DF3  ( x4  x2  x2 b ) DF2  ( x b  x  a x ) DF  a b  x4  2 x2  a x2  x2 b

3
( b3  x3  2 b  3 x4 b  3 x2 b2  3 x4  3 b2  x3 b  x6  x5 ) DF2
x ( b  b2  x2  2 x2 b  x3  x4 )
 x DF
L6 := DF 
 b3  3 b  3 x4 b  3 x2 b2  2 x4  4 b2  x3 b  x6  x5  x2  2 x2 b
b  b2  x2  2 x2 b  x3  x4
Fan: Kompyuter algebrasi tizimlari
O’qituvchi: T.Djiyanov
II-kurs
7-Mavzu..
va

• L7 := GCRD( L4, L6, [DF, x] );

Buni o'ng yoki chap tomonni ko'paytirishi orqali tekshirish mumkin. Bizning masalamizda biz quyidagiga egamiz:

• rightdivision(L6,L7, [DF,x] );

Ikki holatda ham yuqoridagi amal 0 qoldiqli bo'linmani beradi. Hisobni to'g'riligi quyidagi ko'paytirish orqali tekshirish mumkin:

• collect( L4 - mult( %[1], L7, [DF,x] ), DF, normal );

L7 := DF 
x2  b
x
2
x ( b  b2  x2  2 x2 b  x3  x4 )

 ( x3  2 b  2 x4  2 b2 ) DF
 DF 
b  b2  x2  2 x2 b  x3  x4

• rightdivision(L4,L7, [DF,x] );

 2 x3  4 x b  6 b  x4  2 x2  x b2  2 x3 b  x5


, 0 
[ x3 DF2  x2 DF  x3  a x  x, 0 ]
7-Mavzu..
Fan: Kompyuter algebrasi tizimlari O’qituvchi: T.Djiyanov II-kurs