GIA'I H^E. PHU.O.NG TRNH

185)

Gia'i h^e. phu.o.ng trnh:

dydt =x−2y+ 2 sintHD gia’i:

Phu.o.ng trnh da.c tru.ng co hai nghi^e.m

^λ

^1,2

^=±1

+

^λ

1

=−1

gia'i h^e.:

⁰₀ ⁼³₁ ⁻³₋₁ ^γ_γ

¹¹

₁₂

^⇒γ

¹¹

^=γ

¹²

^{= 1.}

+

^λ

²

^{= 1}

gia'i h^e.:

¹₁ ⁻³₋₃ ^γ_γ

²¹

₂₂

⁼⁰₀^⇒γ

²¹

^{= 3; γ}

²²

^{= 1.}

H^e. nghi^e.m co. ba'n cu'a h^e. thu^an nh^at tu.o.ng u.ng la:

(x

₁

=e

^−t

(x

₂

= 3e

^t

y

₁

=e

^−t

;y

₂

=e

^t

(x(t) =C

₁

e

^−t

+ 3C

₂

e

^t

V^a.y NTQ cu'a h^e. thu^an nh^at:

y(t) = C

₁

e

^−t

+C

₂

e

^t

Bi^en thi^en hang s^o:

(C

₁

⁰

e

^−t

+ 3C

₂

⁰

e

^t

= 0(C

₁

⁰

= 3e

^t

sintC

₁

(t) = 32e

^t

(sint−cost)C

₁

⁰

e

^−t

+C

₂

⁰

e

^t

= 2 sint ⇒C

₂

⁰

=e

^−t

sint ⇒C

₂

(t) =−12e

^−t

(sint+ cost)(x(t) = C

₁

e

^−t

+ 3C

₂

e

^t

−3 cost

V^a.y NTQ:

y(t) =C

1

e

^−t

+C

2

e

^t

+ sint−2 costdxdt = 2x−y+z