This kind of differential equation is the simplest, so-called "differential equation with separated variables". Dx/dt=hx, after sorting out dx/x=hdt, only X on the left and T on the right can be obtained by doing indefinite integral on both sides.

Lnx=ht+C(C is an arbitrary constant)

So if we take both sides as e exponents, we will get X = C' E HT and the constant C'≠0.

Don't forget the initial condition x(t=0)=x0, so C'=x0.

The result is x = x0× e (ht).

In short, any equation that can be sorted out, the variables on both sides of the equal sign, can be solved in this way.