Find a particular solution y_p for the ODE x" + 9x = g(t) where g(t) = 1 0<t<1/2 0 1/2<t<1 Assume that when g(t) is extended to the negative t axis in a periodic manner, the resulting function is even.
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Have a look at example 4 here Pauls Online Notes : Differential Equations - IVP's With Step Functions
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