Thanks for the video it helped me plenty. When you watch this video and the one involving the shortcut method you appreciate why the shorter method is much more convenient.
you told at the beginning of the example that we assume second solution as y = u * y1 but after finding y you treat it as general solution. I couldn't get that. Shouldn't that total expression be the second solution? Because we assumed it as so first.
when you integrated w and x,and added the Ln to only w and x it would have been simpler if you add the ln to the c as well then grouped in this form Ln(c/x) then canceled the Lns with e.
In this method we must have one solution to ODE to find another solution, so if we have one solution for a given ODE the why are we finding another solution ?
Think of the line at the bottom being the general solution y = ysub1(x) + ysub2(x). The goal is to find ysub2(x), and that's one of the terms in the general solution.
What is homogeneous here? I did not understand the term homogeneous aspects here. What exactly homogeneous here? How exactly homogeneous here? Why it is homogeneous differential equations?