Question 1: Solve the following boundary value problems (RVP:): a) x'y"-xy'-dy = 0 subject to y(1) =0, V(7) =0 b) y " tay =0 subject to y'(0) = 0 and y'(L) + yy(L) = 0, y>0 c) y "thy =0 subject to - y '(0) + yy(0) = 0, y'(L) =0, y>0 Question 2: Solve the following non-homogenous partial differential equations: aT a'T a) at + x, subject to the following initial and boundary conditions. T(x,0) = f(x), T(0, t ) = 0, T(1,t) =1 b) du du at ax2 +e ' + e-" cos(3xx) , subject to the following initial and boundary conditions. u(x,0) = f(x), u, (0,t) = 0, u, (1,t) = 0 c) at a 2 , subject to the following initial and boundary conditions. u(x,0) = f(x) , u(0,t) =1, u,(1,t) = A