A Unusual Bessel-like Differential Equation with Negative Sign

[maistral]

Hi. I have this Bessel look-a-like DE (however it has the negative sign on the dependent variable):

My attempt at a solution is by (obviously) trying to transform it into a Bessel DE by multiplying it with x² on both sides, then it would look like the Spherical Bessel differential equation, except that there's that negative sign beside y.

Then what? I have no idea what to do. Can someone tell me what this DE is supposed to look like so I can solve it on my own?

 

[Orodruin]

Hi. I have this Bessel look-a-like DE (however it has the negative sign on the dependent variable):

View attachment 203702

My attempt at a solution is by (obviously) trying to transform it into a Bessel DE by multiplying it with x² on both sides, then it would look like the Spherical Bessel differential equation, except that there's that negative sign beside y.

Then what? I have no idea what to do. Can someone tell me what this DE is supposed to look like so I can solve it on my own?

http://mathworld.wolfram.com/ModifiedSphericalBesselDifferentialEquation.html

 

[maistral]

Got it. Thanks!