Final answer:
The question seems to involve solving a second-order differential equation with initial conditions, but the information provided contains typos. To accurately solve this, we would need the correct form of the differential equation.
Step-by-step explanation:
The student has shared an initial value problem which involves solving a differential equation with certain given initial conditions. The text provided is hard to interpret due to potential typos, but it seems to indicate a second-order differential equation of the form y'' + 3y' + 2y = 4 with initial conditions y(0) = 0 and y'(0) = 1. However, the notation is unclear, and to provide a step-by-step solution, we would require the correct differential equation. If we assume the correct form is the one provided in plaintext, we would solve this by finding the characteristic polynomial, determining the roots, and forming the general solution. From there, we would use the initial conditions to solve for any constants.