The given differential equation is:

$y' - \frac{y}{x} = x^2y^3$

Step 1: Rewrite the equation

We rewrite the equation in standard form for separation of variables or identifying its type: $y' = \frac{y}{x} + x^2y^3$

Step 2: Factor the terms

To simplify solving, consider rewriting the equation: $\frac{dy}{dx} = \frac{y}{x} + x^2y^3$

Alternatively: $\frac{dy}{dx} = \frac{1}{x}y + x^2y^3$

This is a first-order nonlinear differential equation. To solve it, let us explore substitution or separable variables depending on the context.

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Would you like:

1. To explore substitution solutions for $u = y^n$?
2. To explore solutions by reducing the equation into exact forms?
3. A plot or numerical approximation?
4. A simpler or linearized version?
5. Verification through series methods?

One tip: Substitution in nonlinear DEs often reduces complexity significantly.