Can someone show me how to Diff Eq?

[1MileCrash]

Homework Statement

I'm not taking a de class, just curious.

dy/dx = (-5x+10y)/(9x)

y(1) = -2

Use appropriate variable change to solve initial value problem.

Homework Equations

The Attempt at a Solution

So, I'm given the derivative of function y, and want to know the actual function, with the condition that the original function when evaluated for 1 is negative 2, right?

So, I integrate it, but I have two variables. What should I do?

 

[Pengwuino]

Well, you have two variables so you might guess that you're going to have to do two different integrals :)

Typically the first line of attack is determining if a problem is what is called separable. In other words can you get your first order DE to look like

$f(y)dy = f(x)dx$

At this point you would normally integrate both sides and then solve for y(x) with your initial conditions.

I don't think this ones separable, though and the next method is using integrating factors. I suggest checking out http://www.khanacademy.org for some nifty videos on solving DEs

 

[1MileCrash]

So, I'm not allowed to just write it as a function of x? I figured that would be okay since the two variables are just x and y like any normal function, no extra one.

 

[Pengwuino]

What do you mean?

 

[1MileCrash]

If the derivative is:

y = (-5x + 10y) / (9x)

Isn't that the same as

y = (5x) / (9x-10)?

Is that allowed?

 

[Pengwuino]

No, that's not right

$y'(x)=(-5x+10y)/9x$

THAT is the derivative. y'(x) and y(x) aren't the same thing.

 

[1MileCrash]

I figured that made the difference. thanks for the links!

 

[Bohrok]

Since the problem says to use a variable change, you can try u = y/x, then the resulting DE becomes separable.

 

[Pengwuino]

Since the problem says to use a variable change, you can try u = y/x, then the resulting DE becomes separable.

oops didn't even notice that part of the question!