Solve differential equationy '(t) = -3y + 9, y(0) = 4

BolkowN 2021-03-09 Answered

Solve differential equation \(y '(t) = -3y + 9\), \(y(0) = 4\)

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Expert Answer

casincal
Answered 2021-03-10 Author has 10059 answers

\(dy/dx= -3y+9\)
\(dy/dx+3y= 9\)
\(I.F.= e^{\int\ 3dt}= e^{3t}\)
\(D_t(e^{3t}y)= 9e^{3t}\)
\(e^{3t}y=0 \int e^{3t}dt\)
\(e^{3t}y=27e^{3t}+C\)
\(y(t)= 27+Ce^{-3t}\)
now as \(y(0)=4\)
\(y(0)= 27+Ce^0\)
\(C= 4-27\)
\(C= -23\)
\(y(t)= 27-23e^{-3t}\)

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