## First Order Linear Differential Equation

In this theoretical article we will try to solve as easier as possible a generic first order differential equation.
This equation is always there to ruin our days ðŸ˜†
If you try to solve a simple RC circuit is there and waiting for you.
It is quite annoying how many times you will find it at your way so we decided to solve this equation even for people who does not have a lot mathematical knowledge.
Lets start.

This is a generic First Order Linear Differential Equation

${{dy} \over {dx}} + P(x)y = Q(x)$

Another way to remember it is

$y' + P(x)y = Q(x)$

So as you can see it is a first order differential equation since the y function is only derivated once.

## Voltage dividers explained

The voltage divider is a circuit that produces an Vout that is a fraction of an Vin.

The two resistors in series can be seen as a single potentiometer.

This circuit will be heavily used in our website so we have decided to do a standalone article for this circuit.

From the Ohms law we know that V=I*R

From the Kirchhoff's current law (first rule) we knowÂ  Î£I=0 So we have I1=I2+I3

From the Kirchhoff's voltage law (second rule) we know that Î£V=0 So we have Vin=V1+V2

Observe that V2=Vout

## Learn how to make at home an etching solution

The etching is theÂ technique that a strong acid chemical solution "eats" the unprotected copper.

So the etching method can be used for the production of printed circuit boards (PCB) since acid can be used to remove the unwanted copper from a copper clad.
A nice and easy method in order to make printed circuits at home is to use the so called : "toner transfer method". This method will be discussed in another article.
For now keep in mind that you have a copper clad (fr4) with the circuit "printed" (with toner) on it.

So this printed copper board can be etched with an acid solution called etchant.
This acid solution will eat all the unprotected toner and the remained, protected by the toner, copper will be our final printed circuit.