Differential equations can be expressed in the form y'' + 6y' + 5 = 0. To solve, identify roots by rewriting it as R^2 + 6R + 5 = 0 and factoring to find R values of -1 and -5. This represents a case one differential equation, leading to the general solution y = c1 e^{-5t} + c2 e^{-t}. Initial conditions are needed for specific constants c1 and c2 but aren't required for solving this basic form.