Final answer:
The provided differential equation y′−3x4y2=3x4 requires solving for y in terms of x, which may involve separating variables or using an integrating factor. The given solutions do not appear to match the original equation, and further clarification is needed to solve it accurately.
Step-by-step explanation:
The question requires finding the general solution of the differential equation y′−3x4y2=3x4. This is a first-order nonlinear ordinary differential equation. The general solution of such an equation will involve an arbitrary constant, often denoted as c. Solving this differential equation typically involves separating variables or using an integrating factor if it is reducible to a linear equation. Unfortunately, without additional context or clarification, it is challenging to provide a definitive general solution due to potential typos in the provided choices.
Let's assume the equation is separable; the separation of variables would include dividing both sides by y2 and integrating. If an integrating factor is needed, we would first need to manipulate the equation to make it linear, which does not seem feasible here. Given the options provided, none appear to cleanly satisfy the original differential equation provided, so further clarification of the problem would be necessary.