How do I find the general solution of a separable ODE?

[shelovesmath]

I am utterly lost on this problem. This is from Applied Partial Differential Equations by Logan, 2nd edition.

Unfortunately, I can't show any attempted work because I don't even know where to start!

In the example, they are using some sort of method for solving and ODE, and I have no idea what.

I really need help with understanding in words what they want me to do, and baby steps in how to do it.

 

[lippyka]

The problem is: Find the general solution of the ODE $$\frac{dy}{dx}-y^2=0.$$The first step is to try to recognize the form of the ODE and determine what method is best to use to solve it. This equation can be written as a separable equation in the form $$\frac{dy}{y^2}=dx,$$which can be solved using separation of variables. To begin solving, separate the variables on each side of the equation: $$\int \frac{dy}{y^2} = \int dx.$$Integrating both sides gives $$-\frac{1}{y} = x + C,$$where $C$ is an arbitrary constant. Rearranging gives $$y = -\frac{1}{x + C}.$$This is the general solution of the ODE.