The differential equation $\frac{d^3y}{dx^3}+11\frac{d^2y}{dx^2}+24\frac{dy}{dx}-36y = 0$ has auxiliary equation
with roots
Therefore there are three fundamental solutions .
Use these to solve the IVP $$\frac{d^3y}{dx^3}+11\frac{d^2y}{dx^2}+24\frac{dy}{dx}-36y = 0$$ $$y(0) = -6$$ $$y^\prime(0) = 5$$ $$y^{\prime\prime}(0) = 9$$