Differential equation question

[redtree]

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

Homework Statement

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

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

Homework Equations

See above

The Attempt at a Solution

\left[ (1/z) * dz/dx = a*\sqrt{dy/dx} \right] *dx<br /> <br /> Thus,<br /> dz/z = a* \sqrt{dy * dx} <br /> <br /> \int dz/z = \int a* \sqrt{dy * dx}<br /> <br /> ln(z) = \int a \sqrt{dy * dx} <br /> <br /> ??

 

[Дьявол]

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

 

[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?