Contents of this Calculus 2 episode:

Solution method, Multiply by dx, Separation, Integration, General solution, Particular solution.

Text of slideshow

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.

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.

# Separable differential equations

02
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Solution method, Multiply by dx, Separation, Integration, General solution, Particular solution.

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Calculus 2 episode