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Particular solution of the inhomogeneous differential equation Watch

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    Find a particular solution of the inhomogeneous differential equation

    y'' -(a^2)y = (e^(ax))*(cos(bx)) , where a and b are real numbers

    I have found the complimentary function - which is given by the solution to the homogeneous equation , but I am struggling with what the trial function for (e^(ax))*(cos(bx)) should be .

    Thanks for any help .
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    If you had to guess, given what you would try if it were just e^{ax} or \cos (bx), what would you say?
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    (Original post by nuodai)
    If you had to guess, given what you would try if it were just e^{ax} or \cos (bx), what would you say?
    If it were just e^ax , I would use Ce^(ax) , and cos(bx) I would try Csin(bx) +Dcos(bx) , is that what you mean ?
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    (Original post by Matt5422)
    If it were just e^ax , I would use Ce^(ax) , and cos(bx) I would try Csin(bx) +Dcos(bx) , is that what you mean ?
    Yup; so what do you think you should use here? [Hint: they're multiplied together.]
 
 
 
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