simplify the second term in the equation and ignore the dx and dy: (15x^2+y-1)dx-(18y-x)dy=0

To simplify the second term \(-(18y - x)\), remove the negative sign and distribute it inside the parentheses:

\[
-(18y - x) = -18y + x
\]

So, the simplified second term becomes:

\[
-18y + x
\]

The equation without the \(dx\) and \(dy\) terms would then be:

\[
15x^2 + y - 1 - (18y - x) = 0
\]

Would you like to explore how to solve this equation or any specific detail about the simplification process?

Here are some related questions you might consider:
1. How can this equation be solved for \(x\) or \(y\)?
2. What methods can be used to solve exact differential equations?
3. How do you determine whether a differential equation is exact?
4. What are the steps to solve this kind of equation after simplification?
5. How does the form of the equation change if you consider integrating factors?

**Tip:** When simplifying, pay close attention to signs and distribute negative signs carefully to avoid mistakes.

Explore how to simplify the second term in the differential equation (15x^2 + y - 1)dx - (18y - x)dy = 0. Learn key algebraic concepts and theorems about exact differential equations, simplifying expressions, and solving them, suited for Grades 10-12.

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