- #1

rhcp89

- 8

- 4

I would like to is it possible to solve such a differential equation (I would like to know the z(x) function):

[tex] \displaystyle{ \frac{z}{z+dz}= \frac{(x+dx)d(x+dx)}{xdx}} [/tex]

I separated variables z,x to integrate it some way. Then I would get this z(x) function.

My idea is to find such a function f(z) (for the left hand side of above equation) that:

[tex] f(z)dz=\frac{z}{z+dz}[/tex]

And for the right side of this first equation I think I should also find similar function g(x) that:

[tex]g(x)dx=\frac{(x+dx)d(x+dx)}{xdx}[/tex]

If I would get these f(z) and g(x) I could get the wanted function z(x) this way:

[tex]\int f(z)dz=\int g(x)dx[/tex]

I think f(z) ang g(x) can be found as numerical approximations. But how to do it in this specific case?

..............

The right hand side of first equation seems for me as pretty hard to find the g(x) so I simplified it this way (however I am not sure if such methods of transformations are ok):

[tex] \frac{(x+dx)d(x+dx)}{xdx}=\frac{(x+dx)(dx+d^2 x)}{xdx}=\frac{(x+dx)dx(1+d)}{xdx}=\frac{x+2dx+d^2 x}{x} [/tex]

Thanks for your help.