II order homogeneous differential equation solution

[Sourabh N]

I am trying to solve the diff. equation -

a$$\frac{d^{2}x}{dr^{2}}$$ + (br + c/r)$$\frac{dx}{dr}$$ + dx = 0

I got it while solving a variant of damped harmonic oscillation.

Any hints (Frobenius method won't work)

 

[Sourabh N]

a$$\frac{d^{2}x}{dr^{2}}$$ + (br + c/r)$$\frac{dx}{dr}$$ + dx = 0

Sorry, this is the correct eqn.