The differential equation $\frac{d^2y}{dx^2}+12\frac{dy}{dx}+36y = 0$ has auxiliary equation
with roots
Therefore there are two fundamental solutions .
Use these to solve the IVP $$\frac{d^2y}{dx^2}+12\frac{dy}{dx}+36y = 0$$ $$y(0) = 1$$ $$y^\prime(0) = -6$$