(adsbygoogle = window.adsbygoogle || []).push({}); Simple Diff Eq Help

I am trying to solve the following Diff Eq:

[tex]\frac{d^2x}{dy^2}+(\frac{y}{2}-\frac{1}{y})\frac{dx}{dy}=0[/tex]

I tried to solve by setting [tex]\frac{dx}{dy}=z[/tex]

so: [tex]\frac{dz}{dy}+(\frac{y}{2}-\frac{1}{y})z=0[/tex]

I know the general solution to this is:

[tex]z=-e^{-\int{\frac{y}{2}-\frac{1}{y}dy}}\int{0}dy[/tex]

This then yields:

[tex]z=-C_1e^{ln(y)-1/4y^2}=\frac{dx}{dy}[/tex]

And trying to integrate again, Using u-substitution, [tex]u = ln(y) -1/4y^2[/tex]

[tex]du=(\frac{1}{y} - \frac{y}{2}) dy[/tex]

[tex]dy = \frac{2}{2-y^2} du[/tex]

Now, can I leave that y tern in the u-substitution? Or did I make a mistake along the way?

Also, is there an easier way to solve this integral than the path I've taken? Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integration Help

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**