Ecuaciones De La Plaice

Y” + 3Y` + 2Y = COS( 6t )

L (Y”) + 3 L(Y`) + 2 L (Y) = L (COS(6t))

S^2 Y (S) – SY (0) – Y (0)` + 3 (SY(S) – Y (0) +2Y(S) = S .

S^2+6^2

S^2Y (S) – S(1) – 2 + 3 (SY(S)-1)+2Y(S) = S .

〖 S〗^2+〖36〗^2

S^2Y(S) – S – 2 + 3SY (S) – 3 + 2Y (S) = S .

S^2+〖36〗^2

S^2Y(S) + 3SY (S) + 2Y(S)= = S . +S+5

S^2+〖36〗^2

S^2 Y(S)+3SY(S)+2Y(Y)= = S+S( S^2 +36) + S(S^2 +36) .

S^2+〖36〗^2

Y(S)( S^2+3S+2) = = S+S( S^2 +36) + 5(S^2 +36) .

S^2+〖36〗^2

Y(S) = = S+S( S^2 +36) + S(S^2 +36) .

(S^2+36) (S^2+3S+2)

Y(S) = = S+ S^3 +36S + 5S^2 +180 .

(S^2+36) (S^2+3S+2)

Y(S) == 375 + S^3 + 5S^2 +180 . = AS + B. . C D .

(S^2+36) (S^2+3S+2) S^2+36 (S+1) (S+2)

= (AS+B)(S+1)(S+2)+( S^2+36)(S+2)-1D(S^2+36)(S+1)

(S^2+36) (S+1) (S+2)

(AS+B)( S^2+25+S+2)+C(S^2+〖25〗^2+365+72)+D(S^3+S^2+365+36)

(S^2+36) (S+1) (S+2)

(AS+B)( S^2+35+2)+C(S^3+〖25〗^2+365+72)+D(S^3+S^2+365+36)

(S^2+36) (S+1) (S+2)

AS^3+3AS^2+2AS+BS^2+3BS+2B+CS^3+2S^2+36CS+72C+DS^3+DS^2+36DS+36D

(S^2+36) (S+1) (S+2)

AS^3+CS^3+DS^3=S^3

3S^3+CS^3+DS^3=S^3

3S^2+BS^2+2CS^2+D^2= 5S^2

2AS+3BS+36CS+36DS=375

2B+72C+36D=180

A B C D S

1 0 1 1 1

3 1 2 1 5

2 3 36 36 37

0 2 72 36 180

EJERCICIO #2

Y” -6Y´+9Y = 3e^st

L (Y”) -6 L(Y`) + 9 L (Y) = 3L (e^5t

S^2 Y (S) – SY (0) – Y (0)` -6 (SY(S) – Y (0) +9(S) =3 1 .

S-5

S^2 Y (S) – S(-2) – (-1)` - 6 (SY(S) – (-2)) +9Y(S) =3 1 .

S-5

S^2 Y (S) + 2S+1 – 6SY(S) +12+9Y(S) = 3 .

S-5

S^2 Y (S) + 2S+13 – 6SY(S) +9Y(S) = 3 .

S-5

S^2 Y (S) – 6SY(S) +9Y(S) = 3 . - 2S-13

S-5

S^2 Y (S) – 6SY(S) +9Y(S) = 3 -2S(S-5)-13(S-5) .

S-5

S^2 Y (S) – 6SY(S) +9Y(S) = 3 -2S^2 -10S-13S-65 .

S-5

Y(S)( S^2-6S+9) = 3 -2S^2 -10S-13-65 .

S-5

Y(S)= 3 -2S^2 -10S-13-65 . = Y(S) = 3 -2S^2 -10S-13-65 .

(S-5)( S^2-6S+9) (S-5)(-3)(S-3)

= 3 -2S^2 -10S-78 .

(S-5)(S-3)(S-3)

Y(S) = -2S^2-10S-75 . = . A . + . B . + . C .

(S-5)(S-3)(S-3) (S-5) (S-3) (S-3)

Y(S) = A(S-3)(S-3)+B(S-5)(S-3)+C(S-5)(S-3)

(S-5)(S-3)(S-3)

Y(S)=A(S^2-6S+9)+B(S^2-8S+15)+C(S^2-8S+15)

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