How to get started with solving basic Differential Equations? I've just started learning Differential Equations and am having general difficulties with a bit of concepts and on how to actually get started. The problem I have is that the books and sources I find always launch into slope fields, and while I get what a field is and how it works. I don't understand how it relates to a differential equation, and more importantly how to solve them. We started with very basic examples and I am already at a loss of what to do.
Essentially my questions boil down to something like this:


*

*What does a slope field represent? i.e. What are the lines indicating or plotting?


*How do they relate to differential equations?


*What are the general steps to solving a very basic differential equation? Such as: $\frac{dy}{dx} = y + 5 $ ($\frac{dy}{dx}$ = $y'$ right?)

Please keep in mind that I have no knowledge of differentials, just calculus, including mulitvariable. (i.e. Calc I-III in the states).

(1). & (2). Slope field (also called vector field or direction field) is a graphical representation of the solutions of a first-order differential equation. It is useful because it can be created without solving the differential equation analytically.
(3). There are different forms of differential equations, therefore there are diifferent ways to solve them. 
One way, with taht you can solve the equation you wrote is the seperation of variables.
You get at the one side of the equality everything that relates to $y$ and at the other everything that relates to $x$.
Then you integrate.
$$\frac{dy}{dx}=y+5 \\  \Rightarrow \frac{dy}{y+5}=dx  \\ \Rightarrow  \int \frac{1}{y+5} dy=\int dx  \\ \Rightarrow \ln{|y+5|}=x+c $$
Now, to get the solution of the differential equation in the form $y(x)= \dots$, you have to solve for $y$.
