Hurmatli talabalar topshiriqni jurnal nomeri bo’yicha topshiradi. Qo’lda yozib rasmga tushurib pdf qilib joylasin. 19-nomerdagi talaba 1-misolni ishlab ketaveradi

1-topshiriq.
Hurmatli talabalar topshiriqni jurnal nomeri bo’yicha topshiradi. Qo’lda yozib rasmga tushurib pdf qilib joylasin. 19-nomerdagi talaba 1-misolni ishlab ketaveradi.
E’tiborli bo’linglar!!!
1. Drixle doira uchun ichki masalasi. tenglamaning doirada =2 -x-y ( shartni qanoatlatiruvchi yechimini toping.
2. Drixle doira uchun tashqi masalasi. doira tashqaisida R tenglamaning , , shartlarni qanoatlantiruvchi yechimini toping.
3. funksiyaning doirada garmonik funksiya ekanini ko’rsating. r= , argument,
4.
5. u_tt+2u_t=u_xx-u(0_x=0=u|_x=π=0; u|_t=0=πx-x², u_t|_t=0=0.
6. u_tt+2u_t=u_xx-u(0_x|_x=0=0, u_x|_{x= π} =0 u|_t=0=0, u_t|_t=0=x.
7. u_tt+u_t=u_xx(01); u|_x=0=t, u|_x=1=0 ; u|_t=0=0 , u_t|_t=0=1-x
8. u_tt=u_xx+u(0<x<2); u|_x=0=2t, u|_x=2=0 ; u|_t=0=u_t|_t=0=0.
9. u_tt=u_xx+u(0_x=0=0, u|_x=l=t, u|_t=0=0, u_t|_t=0=
10. u_tt=u_xx+x(0_x=0=u|_x=π=0; u|_t=0=sin2x, u_t|_t=0=0
11. u_tt+u_t=u_xx+1(0_x=0=u|_x=1=0; u|_t=0=u_t|_t=0=0.


Ko‘rsatma. Yechimni qator ko‘rinishida qidiring. Izoh. Yechimni yig‘indi ko‘rinishida qidirish mumkin, bu yerda funksiya tenglamani va chegaraviy shartlarni qanoatlantiradi. U holda

12. u_tt-u_xx+2u_t=4x+8e^tcosx (0_x|_x=0=2t, ; u|_t=0=cosx, u_t|_t=0=2x.

13. u_tt-u_xx-2u_t=4t(sinx-x) (0_x=0=3, u_x|_x=π/2=t²+t, u|_t=0=3, u_t|_t=0=x+sinx.
14. u_tt-3u_t=u_xx+u-x(4+t)+cos (0_x|_x=0=t+1, u|_{x= π}= π(t+1) ; u|_t=0=u_t|_t=0=x.
15. u_tt-7u_t=u_xx+2u_x-2t-7x-e^-xsin3x (0_x=0=0, u|_{x= π}= πt ; u|_t=0=0, u_t|_t=0=x.
16. u_tt+2u_t=u_xx+8u+2x(1-4t)+cos3x (0_x|_x=0=t, u|_t=0=0, u_t|_t=0=x.
17. u_tt=u_xx+4u+2sin²x (0_x|_x=0=u_x|_{x= π}=0; u|_t=0=u_t|_t=0=0.
18. u_tt=u_xx+10u+2sin2xcosx (0_x=0=u_x|_{x= π/2}=0 ; u|_t=0=u_t|_t=0=0.