It seems like you've written an expression with some mixed terms. Let me clarify the potential mathematical elements involved:

The expression appears to have a differential term, trigonometric functions, and powers of variables. Here's a possible interpretation of what you intended to write:

\[
\frac{dx}{dy} - x^2 y = - y^4 \cos(x)
\]

This looks like a **first-order differential equation**. Let’s break it down:

- \(\frac{dx}{dy}\): This is the derivative of \(x\) with respect to \(y\).
- \( - x^2 y \): A product of \(x^2\) and \(y\).
- \( - y^4 \cos(x) \): A term involving powers of \(y\) and the cosine of \(x\).

If you're trying to solve this differential equation, one possible approach would involve separation of variables or substitution methods, depending on the specific form.

### Do you want to:
1. Solve this differential equation?
2. Clarify or correct the equation?
3. Explore how to approach solving such an equation?

Let me know, and I can guide you further.

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Here are 5 related questions:
1. What is the general approach to solving first-order differential equations?
2. How do trigonometric functions like \(\cos(x)\) affect the nature of solutions in differential equations?
3. What is the method of separation of variables in differential equations?
4. How are non-linear differential equations different from linear ones?
5. Can we solve differential equations using numerical methods?

**Tip:** For complex differential equations, try identifying if it's linear or separable first, as this determines the method to use.

Explore a detailed solution to the non-linear first-order differential equation dx/dy - x^2y = -y^4cos(x). Learn the key concepts, such as separation of variables, the role of trigonometric functions, and how to approach non-linear equations. This solution is suitable for university-level calculus students.

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