MAT 303 Midterm: 2014mid1b

Problem 5. (7 points) Find the genera solution to the differenialuationy )y

Determine whether the vector field is conservative and. if so. find the genera] potential function. F = cos z, 2y17, - x sin z phi = +c Note: if the vector field is not conservative, write "DNE".

4. Consider the equation: x' = ( ) x (a) Find the eigenvalue(s) and the eigenvector(s) of the above 2 X 2 matrix. (b) Find the genera? solution for the system. (e) Find the solution satisfying x(0) = (). (d) Classify the type of the critical point (0,0) and determine the stability of the system.