Question

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

First order differential equations
ANSWERED
asked 2020-12-05
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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