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).

Watch this video if you are unsure about slope fields. You are basically just plotting the arrows in laymen's terms. There will be a direction and magnitude of an arrow at a point, i.e. a vector: Check out the video below: It may be easier for you to visualize someone actually plotting the slope fields than through text: 
https://www.youtube.com/watch?v=eKXtN0SLNLU
