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Particular solution of the inhomogeneous differential equation

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 .
Reply 1
Avatar for nuodai
nuodai
17
If you had to guess, given what you would try if it were just eaxe^{ax} or cos⁡(bx)\cos (bx), what would you say?
Reply 2
Avatar for Matt5422
Matt5422
OP
Original post by nuodai
If you had to guess, given what you would try if it were just eaxe^{ax} or cos⁡(bx)\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 ?
Reply 3
Avatar for nuodai
nuodai
17
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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