I. Foundation/Comprehension (No technology allowed, show your work!) 1. Every linear system has ( , ) as a critical point (ie. as an equilibrium solution) ... (3 points). 2. Given the 2"d order equation: y" - 3y' + 2y = 10e3x a) Find Vc, the complementary (homogeneous) solution (3 points). b) Find yp, the particular solution (3 points). c) Find the combined solution, given the initial conditions y(0) = 14 and y'(0) = 26 (4 points)3- Solve the following I\" order equation, using the method of Laplace transform (6 points): 3" - 3y = 12;)!(0) = 1 4. Find the gamut! solution to the following system, either by converting to a 2"\" order equation or by using the eigenvalue method {6 points): x' = 50x + 20y y' = 1002: 60y