can someone teach me differential equations

>>8524979
khan academy dot org

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>>8524986

but they're not laced with memes

A differential equation is an equation containing one or more derivatives of one or more variables with respect to one or more independent variables.

The rest is just about how can you manipulate them mathematically to obtain the variables as a function of the independent variables

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>>8524991

can i have an example

>>8524979
y - y' = x

Let's remove the x because we're dumb
y - y' = 0
y = y'
y'/y = 0
ln(y) = const
y = exp(const)
y = C
It's particular solution

Now for general solution
y'/y = x
ln(y) = x^2/2
y = exp(x^2/2)

Solution = general solution + particular solution
Here, solution = exp(x^2/2) + C

>>8524979
>1. Laplace Transforms
>2. MEMES
>3. Fail on half the questions that can't be solved with a Laplace transform

At least that was my experience with the course.

>>8524999

wouldn't y'/y = 1 if y'=y

>>8524999
I forget to add t. engineer for memes
But that's literally how it was presented to us

A man falling with a parachute witnesses two forces: the weight pointing down and the air resistence, pointing up.
Defining the earth direction as positive and using the second Newton's law, we can write:

F=ma
mg-kv = ma

where k is the air resistence constant and v is the speed.

Or we can also write:
mg-kx' = mx''

The air resistence is a force which magnitude depends on the speed therefore the aceleration also depends on the speed.

So the way how speed change depends on the current speed. Therefore you have one variable value depending on the rate of change of another variable, this kind of systems are modeled by differential equations.

>>8525004
Yes
See >>8525005
y - y' = 0
y = y'
y'/y = 1
ln(y) = x
y = exp(x)

General solution is still y = exp(x^2/2)
Here, solution is now = exp(x^2/2) + exp(x)

>>8524999
>>8525011
Disregard both, I completely forgot how to solve differentials equations

Brb, killing myself

>>8525026

is this why engineers are gay?

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>>8525049
I actually happen to be a homosexual, but I don't think it's the reason