3. For the systems described by the equations below, with u(t) as the input and y(t) as the output, determine which of the systems are causal and which are noncausal. (1.5 points) (a) y(t)=H[u(t)]=+¹u(t)dt -1 (b) y(t)=H[u(t)]=¹u(t)dt (c) y(t)=H[u(t)]=u(-t) 4. u(t) = { 1,0 ≤ t ≤ 2 and h(t) (0; otherwise system y(t)=u(t)*h(t); (2) Sketch u(t) and y(t). (1 points) = 8(t − 1) + ½ 8(t − 2). (1) Determine the output of the

Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow shafts, and the black dots are the arrow tips.) ? ✓ | 1. z ' = || a' ? 2. ': = ? 3.' = 4. a: = 11 8] -10 3 1 5 -2 1 -5 -13 10] -10 x2 A x2 с x1 (x2 B 2x2/ D Note: To solve this problem, you only need to compute eigenvalues. In fact, it is enough to just compute whether the eigenvalues are real or complex and positive or negative.

Find two linearly independent solutions of y" + 5xy = 0 of the form y1 = 1+ a3a + a6x® + ... y2 = x + b,x* + byz7 +... Enter the first few coefficients: az = a6 b4 by = || ||

Consider the linear system y' = (a) Find the general solution. Ay with 4 - ( -5₁ 4 ) A

Write the given system as a set of scalar equations. Let x' = col (x1'(), x2 (1), x3'(1)- 0 10 1 2 x' = 0 0 1 x+t - 1 1 -11 4 .... X1 (t) = x2'(t) = X3 (t) =