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

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

Answers (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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