Verity that `y=a/x+b` is a solution of the differential equation `(d^2y)/(dx^2)+2/x((dy)/(dx))=0.`

Explanation

Given,


`y=a/x+b`


Differentiating w.r.t. `x`


`y'=(-a)/(x^2)`` \ \ \ ...(i)`


Differentiating w.r.t. `x`


`y''=(2a)/(x^3)`` \ \ \ ...(ii)`



Multiplying `(a)/(x)` to `(i)` and adding with `(ii)`


`=(a)/(x)y'+y''`


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