# Differential equation question

1. Aug 7, 2009

### redtree

This is not a homework question, but I am posting here so as not to run afoul of the "rules."

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

$$(1/z) * dz/dx = a* \sqrt{dy/dx}$$

where x,y,z are variables and a is a constant.

2. Relevant equations

See above

3. The attempt at a solution

$$\left[ (1/z) * dz/dx = a*[tex]\sqrt{dy/dx} \right] *dx$$

Thus,
$$dz/z = a* \sqrt{dy * dx}$$

$$\int dz/z$$ = $$\int a* \sqrt{dy * dx}$$

$$ln(z) = \int a \sqrt{dy * dx}$$

??

2. Aug 8, 2009

### Дьявол

And are you allowed to do something like:
$$(dz/z)^2 = a^2* dy * dx$$

3. Aug 8, 2009

### g_edgar

(1) I would say: first get rid of the square root, then continue. Those calculations with square roots and bare differentials are questionable.

(2) Since there are three variables (x,y,z), what are you supposed to do? For example: Let y be ANY function of x, plug it in and get a differential equation to solve for z... Would that be good for you?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook