Final answer:
The question contains a typo in the differential equation and lacks sufficient initial conditions to solve the initial value problem definitively in its current form.
Step-by-step explanation:
The initial value problem stated in the question appears to be a differential equation with a small typographical error. Assuming it should read y(4) = 2y'' + y' + 8y' which simplifies to y(4) = 2y'' + 9y'. To solve this problem, we would typically look for a general solution to the associated homogeneous differential equation, and then apply initial conditions to find the particular solution that fits the problem. However, the initial condition provided is not the standard type usually given in such problems, as it lacks the necessary information about the function and its derivatives at a particular value of the independent variable. Consequently, without clarification or additional information, it's not possible to solve this initial value problem definitively.