Maple da differensial tenglamalar

>dsolve(ode, y(x), useint);



Endi uchinchi tartibli bir differensial tenglamani yechaylik:

>deq3:=x*(D@@3)(y)(x)-(D@@2)(y)(x)-x*D(y)(x)+y(x)=1;
dsolve(deq3,y(x));





IV.8. ODTlar sistemasini yechish
Maple ba’zi bir differensial tenglamalar sistemalarsini ham yechadi. Quyida ushbu

chiziqli sistema yechilgan.

> sysdeq := [(D@@2)(x)(t)+2*(D@@2)(y)(t)-x(t)-2*y(t), D(x)(t)+D(y)(t)-x(t)+y(t)];


> dsolve(sysdeq);



Natijaning to‘g‘riligini tekshirib ko‘ramiz:
> odetest(%, sysdeq);



Endi nochiziqli sistemani yechaylik:
> sys2 := [diff(x(t),t) = cos(x(t)), diff(y(t),t) = -x(t)^(1/2), diff(z(t),t,t) = y(t)/x(t)];



> dsolve(sys2);





Bu yerda noma’lum argumentning funksiyasi sifatida topilgan ( ) , noma’lum va orqali, noma’lum esa orqali ifodalangan. Qo‘shimcha ko‘rsatma berib, yechimni ning oshkor (explicit) funksiyasi ko‘rinishida topish mumkin. Buning uchun dsolve(sys2, explicit) buyruqni berish kerak (o‘zingiz bajarib ko‘ring)
Yana bir misol:

sys3 := {diff(x(t),t)=- x(t)*(x(t)+y(t)),diff(y(t),t)=y(t)*(x(t)+y(t))};