Final answer:
To find y as a function of x, assume a power series solution for y(x) and solve for the coefficients of the power series representation of y(x). Determine the radius of convergence of the power series, and find y(x) as a function of x within the interval of convergence.
Step-by-step explanation:
To find y as a function of x, we can start by assuming a power series solution for y(x): y(x) = Σn=0 to ∞ aₙxⁿ, where aₙ is a constant coefficient. Substituting this into the given differential equation and equating the coefficients of like powers of x, we can solve for the coefficients aₙ to obtain the power series representation of y(x).
Next, we need to determine the radius of convergence of the power series. This can be done using the ratio test or the method of Frobenius. Once we have the power series representation and the radius of convergence, we can determine y(x) as a function of x within the interval of convergence.
It is important to note that solving the given differential equation involves advanced mathematical techniques and may require specialized knowledge in differential equations.