Question

can anybdy pls help me in solving this differential equation Y"(r)+(1/r)*Y'(r)+aY(r)=b. where a, b are arbitrary constants. r is variable. boundary condition are Y(t1)=V1 and Y(t2)=V2.

Answer 1

you could think of it as cauchy-euler and solve it that way. you can eliminate and try and get constant coefficients.
or solve using power series.

Answer 2

r^2 +(1/r)r+a

r^2 =−(a+1)

r=±sqrt(−(1+a))

The solution form varies depending on a and is real only for a < -1

Answer 3

This gets you the homogenous solution, then find the particular solution.