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). In a slope field,
the direction of the arrow
at each point
represents the direction of the derivitive
(or slope, hence its name),
and the length sometimes
represents the magnitude of the derivative
at the point.
This enables you
to draw an approximate solution
to the differential equation
starting at any point,
just by following the arrows.
(2). As stated above,
by knowing the slope of
the derivative at each point
(assuming you can compute
$\frac{dy}{dy}$
for any $x$ and $y$),
you can get a feel
for what the solutions look like.
(3). There are many, many, many techniques.
I like integrating factors.
