Final answer:
The question deals with solving a nonlinear differential equation involving a derivative term dy/dx and other variables raised to powers. It is a complex math problem that requires methods like separation of variables, integrating factor, or substitution.
Step-by-step explanation:
The student's question pertains to solving differential equations of a particular form. In the equation, (a) which has a typo and (b) are presumably identical, it asks to evaluate an equation that includes a differential term, dy/dx, and other terms involving x, y, and their powers. Since the provided references and the rest of the question's context do not contribute meaningfully to solving these equations, they seem to be irrelevant. Thus, we will focus on the differential equation (x² + 1)dy/dx + xy = x³y³. This type of equation is nonlinear and does not have a straightforward method for solving. However, solutions to such equations often involve separation of variables, integrating factor, or substitution if it's exact or can be made exact.