# differential equation - beginner question [closed]

If I have a differential equation on the form

$$y = y' \cdot c_1$$

can I freely solve for $$y'$$ and use the solution for

$$y' = y \cdot c_2$$

where $$c_2 = \frac{1}{c_1}$$?

## closed as off-topic by RRL, Saad, Cesareo, metamorphy, José Carlos SantosDec 21 '18 at 12:20

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Yes, of course. Assuming that $$c \in \mathbb R$$ is a constant, then if $$c \neq 0$$ :
$$y = y' \cdot c \Leftrightarrow y' = y \cdot \frac{1}{c} \equiv y \cdot c$$
Since $$c$$ is an arbitrary constant, any expression of it will also be a constant, so you can always "manipulate" it to be just $$c$$. Note that only if you have some certain restrictions for $$c$$, then you will need to take these in mind on how they affect the expression $$1/c$$.