Final answer:
The student's question refers to solving a Bernoulli's differential equation, which usually involves separation of variables or using the Bernoulli equation method. However, the additional given information and context does not match the problem at hand, which could indicate either a misunderstanding of the problem or a typo in the question.
Step-by-step explanation:
The student's question involves solving Bernoulli's equation: dy/dx + y/(x-1) = 4(x-1)sqrt(y), given x > 1. The differential equation is separable, meaning it can be rearranged so that all terms including y are on one side and all terms including x are on the other side. Unfortunately, without additional context or clarification, the references to other equations and variables provided cannot be directly applied to solve this Bernoulli's equation. Bernoulli's equation in fluid dynamics typically relates the pressure, velocity, and height of fluid at different points along its flow and is expressed as:
P + 1/2ρv^2 + ρgh = constant
where P is the fluid pressure, ρ is the fluid density, v is the fluid velocity, g is the acceleration due to gravity, and h is the height above some reference point. For the Bernoulli's equation provided in the question (a differential equation), we would generally look to use techniques like the separation of variables or the Bernoulli differential equation method to solve it.