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equation diff�rentiel

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equation diff�rentiel Powered By Docstoc
					                                                ‫ــــــ ــــ ـــــ‬       ‫ا ـــ ـــ ــــ د ت ا ــــ ـــــ ــــــ‬
         y = λe              − ax
                                         ‫ا ا م‬                      a∈R                    y '+ ay = 0                       ‫ت‬            ‫ا و‬         ‫ا‬                ‫ا‬            ‫د ا‬
                                                                                                                                                                                      :
                                                                                                                                                                                               ‫ا‬

                                          λ ∈R

                        r2 ‫ و‬r1                                     ‫ة‬        ‫د ا‬                  ‫ا‬   ∆>0                                                                           ‫د ا‬        ‫ا‬
                        (λ ; µ ) ∈ R        2
                                                 y = λe         r1 x
                                                                        + µe      r2 x
                                                                                                                                                                            ‫ا‬                  ‫ا‬
                                                                                                                                                                           ‫ت‬                       ‫ا‬
                                                                                                      ∆=0
                                                                                                                                 :‫ة‬   ‫د ا‬         ‫ا‬
                           r ‫ا‬       ‫و‬                          ‫ة‬            ‫د ا‬              ‫ا‬                              r 2 + ar + b = 0
                                                 y = ( λ x + µ ) e rx                                                                                          y"+ay'+by = 0
                      ( λ ; µ ) ∈ R2                                                                                             ∆ = a − 4b                            ( a ; b) ∈ R2
                                                                                                                                          2



p ± iq                       ‫ا‬                            ∆<0   ‫ة‬            ‫د ا‬              ‫ا‬
                  y = ( λ cos(qx) + µ sin(qx) ) e ( ( λ ; µ ) ∈ R )          px                                   2



                    = δ cos ( qx + θ ) e ( (δ ; θ ) ∈ R ) px                                  2



                        ( E ) : y "+ ay '+ by =                     f ( x) ‫و‬             ( E ) : y '+ ay =                   f ( x)                       :        ‫ف‬                     ‫د ا‬       ‫ا‬
                  .( ( E )       ‫د‬                  ‫د ا‬         ‫)ا‬           ‫ف‬           ‫ون‬           ‫د‬             (E)
                                                                                                                      y0 ‫و‬            ‫د‬          ‫ص‬                 Z

              .        ‫ف‬         ‫ون‬                 ‫د ا‬                  y−Z              ‫ا ا‬              y = Z + y0 :               ‫( ه‬E)           ‫د‬            ‫ا م‬          ‫ا‬
                                                                                  :‫ا ص‬                ‫ا‬
                             ‫ا ص‬            ‫ا‬                                                                 ‫د‬   ‫ا‬                                   f ( x)               ‫فا‬        ‫ا‬
                                                                                              y '+ ay = f ( x)
          f ( x)           ‫ه در‬            ‫ود در‬          Z
                                                                                         y "+ ay '+ by = f ( x)                                               ‫ود‬           f ( x)
                                                                                              y + ay = f ( x)
          0            0                                                                          "           '
         d Z = d f +1 :                            ‫ود‬       Z

     ( A; B ) ∈ R 2 ‫ ؛‬Z = ( Ax + B ) e
                                       βx

                                                                                           y '+ ay = f ( x)
                                                                                                                                              (α ; β ) ∈ R 2               f ( x) = α e β x
( A; B; C ) ∈ R3 ‫ ؛‬Z = ( Ax + Bx + C ) e
                                           2                            βx
                                                                                    y "+ ay '+ by = f ( x )

     Z = α cos (ω x ) + β sin (ω x )                                                          y '+ ay = f ( x)                            f ( x) = A cos (ω x ) + B sin (ω x )

                           (α ; β ) ∈ R 2                                                y "+ ay '+ by = f ( x)                                   = k cos (ω x + ϕ )

                                                                                     :        ‫وط ا‬        ‫ا‬
                             . ‫ا ا‬                         ‫ا وط ا‬                                 ،
                                                                                                  ‫د‬    ‫وط‬ ‫أو ا‬   ‫د‬
                                         ‫ا‬     ‫ا‬        ‫و ا د‬                       ‫ط وا‬      ‫ن ا وط ا‬     ‫ا و‬     ‫ا‬                                               ‫د‬        ‫ا‬
                             ‫ا م‬           ‫إ ءا‬          ‫ا وط إ‬                        ، ‫وط‬        ‫ف ن‬           ‫د‬
                                            .‫ف ن‬        ‫ا د ون‬                     +‫ف ن‬     ‫د‬    ‫ص‬      =‫ا م‬   ‫ا‬

				
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