First Order Differential Equations.

First order differential equations are a lot more complex than ordinary differentials, the best way to identify a first order is shown below.

An example of this in context is shown below with step by step instructions of how to get from the "General Solution" to the "Particular Solution" using the starting condition.

Getting from the General to Particular solution is just the process from using the starting condition to calculate the arbitrary constant. 

The second example is a more complex issue which involves separating the variables to get the final solution. This is not necessarily the most ideal way in a mathematical world, but in terms of engineering it can be done this way. Mathematicians however may disagree with this step.