Eigen Function: Show that the boundary-value problem y”+λy=0, y(0)=0, y(L)=0.

Eigen Function: Show that the boundary-value problem y”+λy=0, y(0)=0, y(L)=0.

Description: Error in video at beginning part-

y”=0 implies y=c_1t+c_2 then we have a ‘non-trivial solution’ so we would then have to show, as you stated, c_1=c_2=0 therefore we have to solve the system 0=c_1L+c_2, and 0=c_1(0)+c_2, which gives us c_1=c_2=0 thus proving that y=0, the ‘trivial solution’ is the only solution.
I don’t know why I did that first part like that. I will have to redo it. Thanks for pointing that out. I was solving like 50 problems that day. I think, I just had a brain-lapse 🙂

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