The reason is that differential equations are often used to describe processes where the variable is time, commonly denoted by t.

If we denote the variable by t and the function by x, then the equation will be:

In this case the symbol for differentiation is a dot.

And now, let’s see how to solve these equations.

Let’s see what we can do about this one.

is replaced by

Multiply by dx.

Now comes the separation: move all y terms to the dy side, and move all x terms to the dx side.

Integrate both sides to get the solution.

In this case it is enough to have +C only on one side.

GENERAL SOLUTION:

If constant y were zero, then here we couldn’t have done the division.

Let's see whether y=0 is a solution

It seems like it is.

PARTICULAR SOLUTION:

We get the particular solution if we give C a fix value.

It would be particularly satisfying to get a solution where y(0)=666

Here is another equation, let’s try this one, too.

Now, we get rid of the logarithms.

There is such a thing as

This way, bye-bye logarithm.

Here, C is some constant value, therefore ec is another constant, let’s call it D.

Now we have to check whether y=0 is a solution.

It seems like it is.

Here, too, the particular solution means that we fix the value of D to some number.

Let’s assume we want to hold.

Here is something more entertaining.

There is such a thing as , this way, bye-bye tangent.

Well, this seems to be done.

And now let’s see another type of differential equation.