The discussion centers on the rearrangement of the differential equation \(x^2 + \frac{dy}{dx} + xy = 1\). The original poster attempts to isolate \(\frac{dy}{dx}\) using algebra, suggesting \(\frac{dy}{dx} = \frac{x^2}{xy}\), which is incorrect. The community emphasizes the need for a solid understanding of algebraic manipulation before tackling differential equations, highlighting the importance of correctly applying algebraic principles in this context.
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whiskybrah said:I'm completely new to differential equations. I'm just doing random problems online about them. One simple problem asks to re-arrange the following so that the x's and y's are all on one side:
$$x^2 + dy/dx + xy = 1$$
Can I just use algebra to do it? Like:
$$ dy/dx = x^2/xy $$