The problem involves solving the nonlinear differential equation dy/dx + y/x = y²x. By substituting 1/y² and simplifying, it transforms into an equation involving t as -1/y. Differentiating with respect to x leads to rewriting the original equation in terms of dt/dx and integrating factors are applied using e^(∫p dx). The solution is derived step-by-step by calculating integrals, applying properties of logarithms, and incorporating constants for generality.