Unusual Bessel-like Differential Equation with Negative Sign

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

2pql7i8.png


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? :nb) 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?
 

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maistral said:
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? :nb) 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