Differential Equations of the form $\frac{dy}{dx} = g(y)$

The next differential equation that we're going to explore is different to what we've seen before, because we're now going to have a relationship between the derivative and the solution. For example, we might want to solve the differential equation

$$\frac{dy}{dx} = y$$

It doesn't look like we can use any of the techniques we've seen so far, because we don't know what $y$ solution is yet!

However, we will see that we can use some of the techniques from the Change of Variables Theorem and integration by substitution to find a way around this and determine the family of equations which satisfy this differential equation.

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