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I have read that, if you given a differential equation [itex]\frac{dy}{dx} = f(x,y)[/itex], and can write it in the form [itex]\frac{dy}{dx} = h(x)g(y)[/itex], then you can proceed with the following steps:

[itex]\frac{dy}{g(y)} = h(x)dx[/itex]

integrating

[itex]G(y) = H(x) + c[/itex]

Why are these steps vaild? I thought that one was not supposed to regard [itex]\frac{dy}{dx}[/itex]. I have heard that you can regard it as a fraction, because, before taking the limit, you can manipulate the fraction [itex]\frac{\Delta y}{\Delta x}[/itex].

Could someone please help?

[itex]\frac{dy}{g(y)} = h(x)dx[/itex]

integrating

[itex]G(y) = H(x) + c[/itex]

Why are these steps vaild? I thought that one was not supposed to regard [itex]\frac{dy}{dx}[/itex]. I have heard that you can regard it as a fraction, because, before taking the limit, you can manipulate the fraction [itex]\frac{\Delta y}{\Delta x}[/itex].

Could someone please help?

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