What is a solution to the differential equation #dy/dx=y#?
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:
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.
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
So there is our general solution: Any constant multiple of