English: So the left hand side are functions of r, and the right hand side are functions of θ so this should be a constant(λ) okay, unless they are constant it cannot be same because two functions of two different independent variables r and theta, so now the Laplace equation becomes two ordinary differential equation, one is r²R^(″)(r) + rR^(′)(r) + λR(r) = 0, for r₁ < r < r₂ and the other is $- \left( \frac{r^{2}R^{''}(r) + rR^{'}(r)}{R(r)} \right) = \frac{ϴ^{''}(\theta)}{ϴ(\theta)}$.
Telugu: కాబట్టి ఇప్పుడు లాప్లాస్సమీకరణం రెండు సాధారణ డిఫెరెన్షియల్ (differential) ఈక్వేషన్ అవుతుంది, ఒకటి r1 <r <r2 కోసం r²R^(″)(r) + rR^(′)(r) + λR(r) = 0 మరియు మరొకటి ϴ^(″)(θ) − λϴ(θ) = 0 , 0 ≤ θ ≤ 2π కోసం.