Quick Differential Equations Question

[jofree87]

xy'' + y' = 0

Is it ok to multiply this whole equation by x to make it a cauchy-euler equation?

 

[rock.freak667]

Why not just put w=y' and then solve using an integrating factor?

 

[jofree87]

Because this equation is under the cauchy-euler section of my book, so I am trying to figure out how it is done even though its not linear. Does anybody know if its possible to solve this as a cauchy-euler equation?

 

[rock.freak667]

In that case, I believe you can multiply throughout by x and solve it so.

 

[vela]

Actually, the diff. eq. is linear. Why do you think it's not?

 

[LCKurtz]

xy'' + y' = 0

Is it ok to multiply this whole equation by x to make it a cauchy-euler equation?

Definitely yes, although as others have pointed out, that isn't the only way. But it is easy and quick.