Please help answer the following questions

Instructions Complete these problems on a separate sheet of paper (or on a tablet/iPad). Your work should be neat and the problems should be completed in the correct order. Submit the assignment as a PDF on Blackboard. You may use your calculator or an online app to find the coefficients in Problem 5. Make sure that your answer includes the linear system you used to find your coefficients. Problems 1. Consider the following linear system of ODEs: x1 =721 +512 - 913 + 8e-3t 12 = 41 + $2 + 13 x3 = - 212 + 313 + 3e-3t (a) Is the system homogeneous? If no, identify f(t). (b) Write the system in matrix form. 2. Write the linear system of ODEs without the use of matrices: 3. Determine whether ( t) = - e-3t/ 27 2e-3t/2 is a solution to the linear system in Problem 2. 4. Find the Wronskian of $1 = _ and $2 = [3est ] 2est . Is {#1, 12} a fundamental set of solutions? 5. Consider the linear system of ODEs: Given that $1 = CO F and a2 = -5t is a fundamental set of solutions : (a) What is the general solution? (b) Find the solution that satisfies the initial conditions: *(0 ) = cs Scanned with CamScanner