Final answer:
To solve the given differential equation y′′+8y′+16=0, we can use the characteristic equation method. The solution is y=C1e^(-4x)+C2xe^(-4x), where C1 and C2 are constants.
Step-by-step explanation:
The given differential equation is y′′+8y′+16=0.
To solve this equation, we can use the characteristic equation method. Assuming the solution is of the form y=e^(rt), we substitute it back into the equation. This gives us the characteristic equation r^2+8r+16=0.
Using the quadratic formula, we find that r=-4. Substituting this value into the general solution y=C1e^(-4x)+C2xe^(-4x), where C1 and C2 are constants, we get the solution to the given differential equation.