Final answer:
The student is tasked with solving a differential equation where variables need to be separated and integrated to find the function y(x) that satisfies the initial-value problem.
Step-by-step explanation:
The question asks to solve an initial-value problem involving a differential equation of the form y' + (1/3)*y = (1/3)*(1 - 2x)*(y⁴). Solving this equation typically requires separating the variables, integrating both sides, and then applying the initial condition to find the particular solution. The specifics of solving such a differential equation are not provided, but they would follow a mathematical process involving the use of integration techniques and potentially substitution methods to find the function y(x) that satisfies the equation. Without the actual initial condition provided, a general solution methodology is suggested.