Problem 2 () Find the Fourier transform f, the Fourier cosine transform Cf, and the Fourier sine transform Sf of f(x) = ce-1-1 por sinar), (ii) For all positive real numbers a, b, determine the value of Jo (22 + b)2 dr. Jo Dato) (iii) Solve the BVP for the Laplace equation in the quadrant {(x,y): 0, y >0}, Au=0, u(3,0) = re-lel, 2>0, u(0,y) = ye-lyl, y>0. Hints: Write u = ul + up with Auj = Auz = 0 and u1(0,y) = 0 = u(2,0). Use Fourier sine transform. Your final answer for u may be in the form of an integral representation. Problem 2 () Find the Fourier transform f, the Fourier cosine transform Cf, and the Fourier sine transform Sf of f(x) = ce-1-1 por sinar), (ii) For all positive real numbers a, b, determine the value of Jo (22 + b)2 dr. Jo Dato) (iii) Solve the BVP for the Laplace equation in the quadrant {(x,y): 0, y >0}, Au=0, u(3,0) = re-lel, 2>0, u(0,y) = ye-lyl, y>0. Hints: Write u = ul + up with Auj = Auz = 0 and u1(0,y) = 0 = u(2,0). Use Fourier sine transform. Your final answer for u may be in the form of an integral representation