Final answer:
To solve the given initial value partial differential equation, one could use several methods to find a continuous solution that fits the conditions, likely involving steps to isolate and integrate functions of x or y.
Step-by-step explanation:
The question asks for the solution to an initial value partial differential equation. To solve this, one typically uses methods such as separation of variables, the method of characteristics, or transforms depending on the specific form of the equation. Considering the SEO keywords "initial value problem," "partial differential equation," and "solution," one approach could involve assuming a potential function or using a probabilistic interpretation to find a continuous function that satisfies the given conditions. Calculations would involve integrating to find expressions involving y as a function of x or vice versa, following the steps required to isolate the function and its derivatives that are needed to satisfy the differential equation.