Schaum Serisi Diferansiyel Denklemler Pdf 55 -

Guess ( y_p = A e^{3x} ) [ y_p' = 3A e^{3x}, \quad y_p'' = 9A e^{3x} ] Substitute: [ 9A e^{3x} - 9A e^{3x} + 2A e^{3x} = 6e^{3x} ] [ 2A e^{3x} = 6e^{3x} \implies A = 3 ] [ y_p = 3e^{3x} ]

Solve ( y'' - 3y' + 2y = 6e^{3x} )

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Characteristic equation: [ r^2 - 3r + 2 = 0 \implies (r-1)(r-2) = 0 \implies r = 1, 2 ] [ y_h = C_1 e^{x} + C_2 e^{2x} ] Guess ( y_p = A e^{3x} ) [