Final answer:
The problem is a differential equation from mathematics at the college level, requiring clarification of the equation terms. Once clarified, standard methods such as separation of variables or using an integrating factor may be applied, depending on the form of the equation.
Step-by-step explanation:
The question appears to be a differential equations problem from the field of mathematics, possibly at the college level, where a student is seeking help with solving an equation involving derivatives. As the original question contains typos or irrelevant parts that we are asked to ignore, I'll address the standard form of a first-order linear differential equation and the concept of separation of variables.
To solve an equation of the form 4x dy - y dx = x'^2 dy, you would first clarify the meaning of x' and then proceed with the appropriate method, which could involve separating variables or integrating factors, depending on the actual form of the equation. However, without clear context or the correct equation, providing a step-by-step solution is not feasible.
If we are dealing with separation of variables, a common method to solve first-order differential equations, it would involve rearranging the equation to isolate all terms involving y and dy on one side and all terms involving x and dx on the other side, and then integrating both sides.