Different Equations problem

Math 246 Homework Assignment Six Do the following problems showing all your work. Be sure to submit your solutions in PDF format. (Point values are given in the square brackets.) 1. [5] Use elimination to solve this system for x (t), y (t), z(t): x' =x+2y -z V=xtz 2' = 4x - 4y + 52 (HINT: Think of x' (etc.) as the differential operator "Dx" and try and obtain equations with a single differential operator and its variable to solve.) 2. [5] Draw a phase plane diagram (portrait) for the following system: dx =( -x)(y - 1) dy dt = (x - y)(x - 1) 3. [4] Find a general solution (y(x)) to the equation y"" - 2y" - 5y' + 6y = 0. 4. [3] Express following system in matrix notation: dx dt -=xty+z dy dt -= 22 - x dz dt = 4y 5. [3] Express the following equation in the matrix for x' = Ax + f. day dy dx 3 dx -+ y = cos x 6. [5] Solve the system, dx dt = 12 21x with initial conditions, x (0) = [1,]