Steady state temp. distribution

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Homework Statement


Diagram of a rectangular region of width a and height b with boundary temperatures: left edge labeled T0, top and bottom edges with linearly varying temperature from T0 at the left corners down to 0 at the right corners, and right edge labeled 0.


Homework Equations


ıt is nonhomog type ,2D heat conduction problem

The Attempt at a Solution


I don't understant To parts so I couldn't attemp a solution.
 
Shouldn't we found T(x,y)
and for upper and lower parts should I write as afuction of x To(x) and then define new temperature variable Q=T-To to eliminate nonhomog on the left side
 
What about the upper and lower boundaries?
Bc should be x=0 t=to
X=b/2 t=to
Y=0 dt/dy =0
Y=b t= to(x)