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PDE using separation of variables

after solving X"+w2X=0X"+ w^{2}X= 0 and T′+w2T=0 T'+w^2T=0
is X=Acos(wx)+Bsin(wx) X=Acos(wx)+Bsin(wx) and T=Ce−w2t T= Ce^{-w^2t}
something that we should just know?
Reply 1
Avatar for Serano
Serano
11
Original post by elldeegee
after solving X"+w2X=0X"+ w^{2}X= 0 and T′+w2T=0 T'+w^2T=0
is X=Acos(wx)+Bsin(wx) X=Acos(wx)+Bsin(wx) and T=Ce−w2t T= Ce^{-w^2t}
something that we should just know?


They are both the ODE eigenvalue problems you get upon assuming the solution to the heat equation (I take it?) on an interval is of the form X(x)T(t)... they're pretty standard linear ODEs and it is generally assumed at most university courses that a prequisite for a PDE module would be an ODE module. If not, I suggest you look up linear ODEs (it's fairly trivial stuff)
Reply 2
Avatar for zeratul
zeratul
1
Original post by Serano
I suggest you look up linear ODEs (it's fairly trivial stuff)


More precisely 2nd order linear odes with constant coefficients (for the first one, X) and separation of variables (for the 2nd, T)

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