Thread: Solve (x^2)*u_x + (y^2)*u_y = (x+y)u

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)

Originally Posted by Waikato

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)

Characteristic equation



so



or giving

Solution:

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")