Persamaan Diferensial Orde II

PDB Orde II PDB Orde II

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Metode koefisien tak tentu Metode koefisien tak tentu

  r(x) y _p r(x) = e ^mx y _p = A e ^mx r(x) = X ⁿ y _p = A _n

  X ⁿ + A _n-1

  X ^n-1 +…….+A ₁ X + A r(x) = sin wx y _p = A cos wx + B sin wx r(x) =cos wx y _p = A cos wx + B sin wx r(x) = e ^ux sin wx y _p = e ^ux (A cos wx + B sin wx ) R(x) =e ^ux cos wx y _p = e ^ux (A cos wx + B sin wx ) ( /

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Latihan Latihan

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Metode Variasi Parameter Metode Variasi Parameter

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  y y _{2 1} r ( x ) y ' ₂ y r ( x ) y ' r ( x ) _{2 1} y r ( x ) ₁

  = = − u ' u dx = = v ' v dx y y _{1 2} W y y _{1 2} W y ' y ' _{1 2} y ' y ' _{1 2} y y _{1 2}

  6 W =

  y y ₁ ' ' ₂ Contoh Contoh

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  x − sin 1 cos x x x sin tan

  = − x − x dx = − dx = − (sec cos ) dx u = − dx x cos cos x

  1 Contoh (Lanjutan) Contoh (Lanjutan) x x x sin tan sec ln

• − = + − = dx x dx x cos sec = dx

  x x v 1 tan cos

  = dx x sin x cos

  − =

  / # #

  ( ) x x x x x x x y _p cos sin cos sin cos tan sec ln

  − + + − =

• − =

  #

  ( ) x x x cos tan sec ln

• − + =

  ( ) C x x x x x C y cos tan sec ln sin cos _{2 1}

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  3 3 sec 3 sin ² − = dx x

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₂

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  3 sin 3 tan 3 sec ln

  9

  1 3 cos

  1 3 sin

  1 3 cos 3 tan

  9

  1 3 cos _{2 1}

  ( ) x x x x x x

  3 sin 3 tan 3 sec ln

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  Contoh (Lanjutan) Contoh (Lanjutan) x x

  3 tan

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  1 − = − = dx x dx 3 sec

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  1 ₂ = dx x x v

  3 sin 3 tan 3 sec ln

  3 3 sec 3 cos ² = dx x

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  1 x x

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  ( ) x x x x x x x y _p

• − =
• − + =

Latihan Latihan 1. y” + y = cosec x cot x 2. y” + y = cot x x e 3. y” – 3 y’ + 2y = x

• e

  1 − 2 x e e 4. y” + 4 y’ + 4 y =

  2 x 5. y” + 4 y = 3 cosec 2x

  6. y” + 4 y = 3 cosec x 7. 4 y” + y = 2 sec (x/2) x e 8. y” – 2y’ + y =

  2

• 1 x

  Penerapan dalam Rangkaian Listrik Penerapan dalam Rangkaian Listrik

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Rangkaian RLC Rangkaian RLC

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  ^-

Latihan Latihan

  % = BC( ) '1 *

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Latihan Latihan

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