MHB Can Algebra Alone Rearrange This Differential Equation?

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The discussion revolves around rearranging the differential equation \(x^2 + \frac{dy}{dx} + xy = 1\) to isolate the variables. The original poster, new to differential equations, questions whether algebra alone can achieve this. A response suggests that while algebra can be used, there are mistakes in the proposed rearrangement, indicating a need for a better understanding of algebraic manipulation. The conversation emphasizes the importance of revisiting algebra fundamentals before tackling differential equations. Overall, a solid grasp of algebra is essential for correctly rearranging and solving such equations.
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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:

$$ dy/dx = x^2/xy $$
 
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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:

$$ dy/dx = x^2/xy $$

Welcome to MHB!

Yes but maybe revisit algebra first. There are several mistakes here and it isn't clear what you've done. Mind expanding? :)
 

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