Solve the following initial and boundary problem. Check your answer by substituting and explain all the steps: Uryz (y, 2) = + xy 2 u (1, y, z) sin y+, u, (1, 0, 2) = 2 3 Uzz (x, 0, 2) = 22 + cos2, uzy (x, y, 1) = e + cosy. xy (2-1)- (2-1)= y (21) (2-1) Given the differential equation y Oy x+cosr Or = 0, y > 0. (15 Marks) b1. Use the method of characteristics to find a solution to the above equation, and check your answer. (10 Marks) b2. Find a solution that satisfies the boundary conditionu (0, y) = y + Iny. (5 Marks)