4 - Solving Basic Differential Equations with Integration

The simplest form of a differential equation is the most basic one, where the derivatives and variables are all each on one side.

This is to say that sometimes, you can manipulate, or should manipulate differential equations to make them easier to solve, or to just be able to solve them at all.

This isn't really supposed to happen in mathematics, but, in the context of differential equations, you can play around with the dx,dy parts, moving them around to make things make sense.

Consider this:
This essentially just says that the derivative of y with respect to x is some function of x.

"Okay, what am i supposed to do with this..?"

Try moving around dy or dx. Or, just move dx.
Something there looks really familiar...

Yup!
Since you only have that dy there, you just get y, and for f(x)dx you get the primitive and a constant c:
The core of these differential equations is the general solution that differs by a constant. This is why it was so oddly important to always add that +c at the end of integration.

Before we get to ACTUALLY solving these, we need to understand one more topic.

5 - Existence and Uniqueness of Solutions to Differential Equations

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