First Order Differential Equation : $$ \dfrac{df(t)}{dt}+ a f(t) = \dfrac{\sin(b t)}{\pi t} $$ $$ f(t)=? $$ I try to find solution in this way $$ \dfrac{dy}{dt}+ P(t) y = Q(t) $$ $$ y=e^{-\int P(t)dt} [\int Q(t) e^{\int P(t)dt} dt+c] $$ $$ y=e^{-at}[\int \frac{e^{at}sin(bt)}{t} dt+C ] $$ I can't Find solution for the integral. plz help me. thx so much
First Order Differential Equation : $ \dfrac{df(t)}{dt}+ a f(t) = \dfrac{\sin(b t)}{\pi t} $
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ordinary-differential-equations
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1Could you atleast show some efford in your questions? Show what you have tried instead of just giving us some homework assignment. – 2012-12-21
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0At least the homogeneous solution should be easy to find.. – 2012-12-21
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0You can look at my last edit for some information about the integral. Were you expecting it to be elementary? – 2012-12-21