Solve the following initial value problem dydt 4y 16 y0 9

Solve the following initial value problem: {dy/dt = -4y + 16 y(0) = 9 Solve the following initial value problem: y(t) = ?

Solution

dy/dt = -4(y-4)

Seperating the variables we get

dy/(y-4) = -4dt

Integrating both sides we get

ln(y-4) = -4t + C

Using the initial condition y(0) = 9

ln(5) = -4(0) + C

Hence the value of C = ln(5)

Therefore the final solution will be

ln(y-4) = -4t + ln5