# What is the general solution of the differential equation dy/dx+2y=0?

What is the general solution of the differential equation $\frac{dy}{dx}+2y=0$?
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zagrebova1c
We have:

$\frac{dy}{dx}+2y=0$

We can just rearrange as follows:

This is a first Order Separable Differential Equation and "separate the variables" to get

And integrating gives us:

$\mathrm{ln}|y|=-2x+A$

$\therefore |y|={e}^{-2x+A}$

Note that as ${e}^{\alpha }>0\forall \alpha \in ℝ$, we can write

$y={e}^{-2x+A}$