Find a nonzero function such that f′(x)=4f(x)

We want to solve in a general way the given differential equation.

The function we want to get is:

Let's see how to get that function.

we have:

From this we can assume that the function f(x) is an exponential function of the form:

So when we differentiate it, the only thing that happens is that the 4 comes down as a factor:

This is the nonzero function that we wanted, where A can be any real number different than zero.

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