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In this video I will, in case #3, I will solve the differential equation for the theta function (zenith direction, y-z plane) when n=1,l=1, and m(l)=1. From previous video we found f(x)=(1-x^2)^1/2 for l=1 and m(l)=0 thus ThetaFunction(theta)=Asin(theta). So we will substitute sin(theta) back to the original differential equation to see if, indeed, the equation will equal to 0.

Next video in this series can be seen at:
https://youtu.be/jwU4PjeZi1c