Obtain the solution of
(x^2)*u_x + (y^2)*u_y = (x+y)u
(Hint: to obtain a general solution you may need to use the fact that dy/y^2 = (dx - dy)/ (x^2 - y^2)
Are you able to solve this question?
Consider u_t + (v.grad)u = 0 , where grad = upside down triangle, and v is a vector, dotted with the grad symbol.
where v = (-ax, ay) represents 2D stagnation point flow and u = u(x,y,t). Obtain a solution of the Cauchy problem given that u = u0(x,y) at t = 0
(u0 is read as "u naught")