1. Maple Ifoda va ularning turlari

Berilgan topshiriqning bajarilish qismi
1-misol: Quyidagi differensial tenglamaning umumiy yechimini toping:
y(4)+2y'''-2y''=2cosx.
Yechish:
> with(DETools):
DifTeng:=diff(y(x),x$4)+3*diff(y(x),x$3)-
2*diff(y(x),x$2)=2*cos(x);
> dsolve(DifTeng,y(x));
2-misol: Quyidagi Koshi masalasini yechimini aniqlang:
y(4)+2xy'''-2y''=2cosx, y(0)=2, y'(0)=1, y''(0)=0, y'''(0)=0.
Yechish:
> with(DETools):
DifTeng:=diff(y(x),x$4)+3*diff(y(x),x$3)-
2*diff(y(x),x$2)=2*cos(x);
> BoshShart:=y(0)=-1,D(y)(0)=3,D[1$2](y)(0)=-
4,D[1$3](y)(0)=6;
> dsolve({DifTeng,BoshShart},y(x));
3-misol:
Koshi masalasining yechimini: yy xe y , y(0) 0 5-chi tartibli aniqlikda
darajali qator ko’rinishida yechimni izlash.
> Order:=5;
DifTeng := 


d d
4 4x
y( x) 3 


d d
3 3x
y( x) 2 


d d
2 2x
y( x) 2 cos( x)
y(x)_C2 e( 3/2 x1/2 x 17 )



3 2
17
2
2
_C1 e( 3/2 x1/2 x 17 )



3 2
17
2
2
1 3
cos(x) 1
3 sin(x) _C3 x _C4
DifTeng := 


d d
4 4x
y( x) 3 


d d
3 3x
y( x) 2 


d d
2 2x
y( x) 2 cos( x)
BoshShart:= y(0)-1, D(y)(0)3, (D( 2))(y)(0)-4, (D( 3))(y)(0)6
y(x)



17
102
11
6 e
( 3/2 x1/2 x 17 )



3 2
17
2
2



11
6
17
102 e
( 3/2 x1/2 x 17 )



3 2
17
2
2
1 3
cos(x)
1 3
sin(x) 6 x 9
2
>
dsolve({diff(y(x),x)=y(x)+x*exp(y(x)),y(0)=0},y(x),type=s
eries);
4-misol: Quyidagi Koshi masalasini sonli yechimining grafigini [2; 3] oraliqda
DEplot komandasidan foydalanib chizing:
у'''+3xу''– у'+5x=0, у(0)=1, у'(0)=4, у'' (0)=2.
> with(DETools):
> DifTeng:=diff(y(x),x$3)+3*x*diff(y(x),x$2)-
diff(y(x),x)+5*x=0;
> Bosh_shart:=[[y(0)=1,D(y)(0)=-4,D[1$2](y)(0)=2]];
> DEplot( DifTeng, y(x), x=-2..3, Bosh_shart );
2-misol