# Diff EQNot sure what method to use

1. May 25, 2009

1. The problem statement, all variables and given/known data

In one of my fluids homeworks, I wound up with a DE of the form

$$A\frac{dh}{dt}+B\sqrt{h}+C=0$$

where A, B, and C are known constants. Can I use the integrating factor on this if I divide thorough by the
leading coefficient A and put it in the form

$$\frac{dh}{dt}+\frac{B}{A}\sqrt{h}=-\frac{C}{A}$$

?

I am just not sure how to approach this DE. Any hints are great

Last edited: May 25, 2009
2. May 25, 2009

### dx

This is seperable.

3. May 25, 2009

Okay. Is it separable as is? Because I don't see it? Perhaps a substitution is needed?

4. May 25, 2009

### dx

Yes, just divide by B√h + C, and multiply by dt. You will get

$$\frac{-A}{B\sqrt{h} + C}dh = dt$$

5. May 25, 2009

Wow. I need to brush up on my math, because I still have no idea how you did that. I have no idea how to divide

$$A\frac{dh}{dt}+B\sqrt{h}+C=0$$

by B√h + C

I wouldn't even know where to start. I am trying now. Do you do it term by term? I realize that this is just Algebra, but I guess mt Engineering classes
are veering away from all that goodness

6. May 25, 2009

### dx

$$A\frac{dh}{dt}+B\sqrt{h}+C=0$$

$$B\sqrt{h}+C = -A\frac{dh}{dt}$$

Dividing by B√h + C,

$$1 = \frac{-A}{B\sqrt{h}+C}\frac{dh}{dt}$$

Multiplying by dt,

$$dt = \frac{-A}{B\sqrt{h} + C}dh$$

7. May 25, 2009