y''+9y=30sin(3x)

I'm told to use the method of solving y''+9y=30e^(3ix), but I'm not sure what to do after I find (D-3)(D-3)y=30e^(3ix).

Could I have some help?

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- Mar 7th 2010, 07:51 PMFwahmSecond Order differential equation problem
y''+9y=30sin(3x)

I'm told to use the method of solving y''+9y=30e^(3ix), but I'm not sure what to do after I find (D-3)(D-3)y=30e^(3ix).

Could I have some help? - Mar 7th 2010, 11:21 PMchisigma
In terms of Laplace Transform the particular integral of...

(1)

... is written as...

(2)

... so that is...

(3)

Alternatively [and is is a not confortable job (Thinking)...] You can search for function of the type...

(4)

... that satisfies (1)...

Kind regards