Bai5 PTVPC2 HK2 0506 Web

Bai5 PTVPC2 HK2 0506 Web - BO MON TOAN NG DUNG -

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Unformatted text preview: BO MON TOAN NG DUNG - HBK------------------------------------------------------------------------------------- TOAN 4 CHUOI VA PHNG TRNH VI PHAN BAI 5: PHNG TRNH VI PHAN CAP 2 TS. NGUYEN QUOC LAN (5/2006) NOI DUNG----------------------------------------------------------------------------------------------------------------------------------- 1 PHNG TRNH VI PHAN CAP 2. TRNG HP GIAM CAP 3 PHNG TRNH VI PHAN CAP 2 HE SO HAM 2 PHNG TRNH VI PHAN CAP 2 HE SO HANG GIAM CAP PHNG TRNH VI PHAN CAP 2-------------------------------------------------------------------------------------------------------------------------------------- VD: Giai phng trnh vi phan cap 2: x x x y y cos ' ' ' + = Phng trnh vi phan cap 2: F(x, y, y, y) = BT Cosi: PT chuan hoa + K au ( 29 ( 29 ( 29 = = = 1 ' , ' , , ' ' y x y y x y y y x f y Giam cap c ban: Phng trnh F(x, y, y) = Nguyen tac: at u(x) = ao ham cap thap nhat cua an y ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ' , , : " ' ' ' ' , ' , = = = = u u x F x y x u x y x u y y x F Nghiem tong quat PT vi phan cap 2 cha 2 hang ap so: Nghiem x x x C x C y cos sin 2 2 1- + + = PHNG TRNH VI PHAN TUYEN TNH CAP 2-------------------------------------------------------------------------------------------------------------------------------------- Tuyen tnh (linear): y,y,y bac 1 He so ham, k0 thuan nhat (ve phai): y + p(x)y + q(x)y = f(x) V du: He so hang, k0 thuan nhat (co ve phai): y + py + qy = f(x) V ( 29 1 sin cos sin ' ' ' 2 x x x y e x y xy x + =- + ( 29 3 sin cos 4 ' 3 ' ' x x x y y y + =- + PT thuan nhat tng ng: y + p(x)y + q(x)y = ( 29 2 sin ' ' ' 2 =- + y e x y xy x V du: Tng ng (1): PT thuan nhat tng ng: y + py + qy = V du: Tng ng (3): ( 29 4 4 ' 3 ' ' =- + y y y GIAI PTVP TUYEN TNH C2 THUAN NHAT HE SO HANG ---------------------------------------------------------------------------------------------------------------------------------------------- x k x k tn tq e C e C y 2 1 2 1 . + = x k x k e e 2 1 , s c nghiem 2 PTVPC2 thuan nhat he so hang y + py + qy = 0 PTrnh ac trng k 2 + pk + q = 0 > 0: k 1 k 2 R < 0: N0 phc = 0: k 1 = k 2 R i k i m = = < 2 , 1 2 2 kx kx xe e , s c nghiem 2 kx kx tn tq xe C e C y 2 1 ....
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Bai5 PTVPC2 HK2 0506 Web - BO MON TOAN NG DUNG -

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