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I've recently started studying differential equations. There is one thing I don't understand and of which I simply can't find an explanation.

I'm trying to solve some linear differential equations without using standard solutions.

Say we have the equation:

[tex]\frac{dp}{dt}=0.5p - 450[/tex]

The next step is (according to my book):

[tex](1) \frac{dp}{p-900}=\frac{1}{2} dt[/tex]

All of the next steps that lead to the solution are clear to me. They use the chain rule to integrate, exponentiate, and get: [itex]p=900+ce^\frac{t}{2}[/itex].

But what I don't understand, is why they first write it in the form of eq.(1), and not as, say:

[tex](2) \frac{dp}{.5p-450}=1 dt[/tex] ?

Possibly it's a silly question, but nevertheless, please help me out :) .

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# Simple linear diff.eq.

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