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

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

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

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