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

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

Answers (1)

2021-03-10
\(dy/dx= -3y+9\)
\(dy/dx+3y= 9\)
\(I.F.= e^(int 3dt)= e^(3t)\)
\(D_t(e^(3t)y)= 9e^(3t)\)
\(e^(3t)y= 0 int e^(3t)dt\)
\(e^(3t)y= 27e^(3t)+C\)
\(y(t)= 27+Ce^(-3t)\)
now as y(0)=4
\(y(0)= 27+Ce^0\)
C= 4-27
C= -23
\(y(t)= 27-23e^(-3t)\)
0

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