Partial Differential Equations Questions.

Please answer Q5, Q6 and Q7. Thanks

5. Let u(x, y) be a solution of the equation Au = 0 in R2. Derive the equation under the polar coordinates: x = rcos, y = r sin 0. What is the equation if u(x, y) is just a function r? (Namely, u(x, y) = u(r). 6. Consider a differential equation a (20) 2/" ( x) + b ( xx ) 1/' ( x ) + [ Ac ( x ) + d ( x ) 12 ( 2 ) = 0,0 0, b(x), c(x) and d(x) are known functions, A is a parameter. Find an integrating factor a(x) such that the equation can be expressed as the standard self-adjoint equation: 2 dx [A(x) dy dx + [AB(x) + C(x)]v = 0,0