\(dy/dt= -3y+9\)

\(dy/dt+3y=9\)

\(I.F.= e^(int 3dt)= e^(3t)\)

\(D_t(e^(3t)y)= 9e^(3t)\)

\(e^(3t)y= 9 int e^(3t)dt\)

\(e^(3t)y= 27 e^(3t)+C\)

\(y(t)= 27e^(3t)y\)

now as y(0)=4

\(y(0)= 27+Ce^(0)\)

C= 4-27

C= -23

C= -23

\(y(t)= 27-23e^(-3t)\)

\(dy/dt+3y=9\)

\(I.F.= e^(int 3dt)= e^(3t)\)

\(D_t(e^(3t)y)= 9e^(3t)\)

\(e^(3t)y= 9 int e^(3t)dt\)

\(e^(3t)y= 27 e^(3t)+C\)

\(y(t)= 27e^(3t)y\)

now as y(0)=4

\(y(0)= 27+Ce^(0)\)

C= 4-27

C= -23

C= -23

\(y(t)= 27-23e^(-3t)\)