Problem 2. Let u(x,y)=xex2y2 denote the temperature distribution over the square [2,2][2,2]. a) Run the following MatLab code on you computer and determine the points with maximum and minimum temperature [x,y]= meshgrid (2:0.2:2); u=x,exp(x,2y,2); surf(x,y,u); vieu(2); axis equal; shading interp; colormap jet b) Solve the system u=0 and verify the solution with part a). c) The following MatLab code shows the gradient of u and the contours (level curves) of you [x,y]= meshgrid (2:0.2:2); u=x,exp(x,2y,2); [ux, uy] =gradient(u); contour (x,y,u); hold on quiver ( x,y,ux,uy) Find the equations of the curves that orthogonal to the vector field u (the equations of level curves). d) Find curves y=f(x) such that the derivative of u along the curves satisfies the following condition dxdu=2xu Problem 2. Let u(x,y)=xex2y2 denote the temperature distribution over the square [2,2][2,2]. a) Run the following MatLab code on you computer and determine the points with maximum and minimum temperature [x,y]= meshgrid (2:0.2:2); u=x,exp(x,2y,2); surf(x,y,u); vieu(2); axis equal; shading interp; colormap jet b) Solve the system u=0 and verify the solution with part a). c) The following MatLab code shows the gradient of u and the contours (level curves) of you [x,y]= meshgrid (2:0.2:2); u=x,exp(x,2y,2); [ux, uy] =gradient(u); contour (x,y,u); hold on quiver ( x,y,ux,uy) Find the equations of the curves that orthogonal to the vector field u (the equations of level curves). d) Find curves y=f(x) such that the derivative of u along the curves satisfies the following condition dxdu=2xu