# Solve differential equation dy/(dt)+2y=1

Question
Solve differential equation $$dy/(dt)+2y=1$$

2020-12-06
$$dy/(dt)+Py=Q$$
Hence P=2, Q=1
$$I.F.= e^(int Pdt)$$
$$= e^(int 2dt)$$
$$= e^^(2t)$$
$$y*I.F.= int Q*I.F.$$
$$ye^(2t)= int 1(e^2t)$$
$$ye^2t= e^2t/2+C$$
$$y=1/2+Ce^(-2t)$$

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