# What is a solution to the differential equation #dy/dx=y#?

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If you aren't looking for the *general* solution, but rather just *one* solution, then sometimes you can figure it out for simple differential equations like this by thinking for a second about what the differential equation literally means.

We're looking for a function,

There's one function which you probably learned previously that has exactly this property:

The function

If you're also interested in finding *all* solutions to this DE, (or you're not interested in trial-and-error) then you can solve this DE by separation of variables.

Think of

And then divide both sides by

Now, integrate the left-hand side

Remember to add the constant of integration, but we only need one.

Raise both sides by

Now, pulling the

Since

So there is our general solution: Any constant multiple of

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