How to set up differential equations for algebraic manipulation?

[wetwilly92]

Hey guys,
We skimmed a chapter on differential eqns in my semester 2 calculus class and we have a worksheet to fill out. I'm having trouble setting up the last 3 problems in this sheet.

http://dl.dropbox.com/u/85600/DIFF_HW.PDF"

I'm pretty sure It's all just algebraic manipulation to make the eqns separable, but I'm having trouble "massaging" the eqns into a separable form.

Can anyone help me out?

 

[CompuChip]

For #18, would you be able to solve
$$x \frac{du(x)}{dx} + u(x) = x$$?

For #19, what is d/dx(x² y)?

For #20, the approach looks OK, did you get stuck?

 

[eczeno]

#20 is easier than you are making it. you don't need to solve it to answer the question. y will be decreasing when dy/dx is negative. you have a formula for dy/dx so you just need to find the intervals on which it is negative.

#'s 18 and 19 are not separable. they are linear and first-order, so integrating factors will work (after a pinch of 'massaging' as you so nicely put it).

hope this helps

 

[Evo]

Here's is what is in the link.