3. (3 points each) Consider the initial value problem y" -y" 3y +5y 0 with y(0) 0, y(0) 3, y"(0) 3. (a) Write the third-order differential equation as a system of first-order differential equations, i.e. write in the form uAu where u (ui, u2, uz)7 andy, (b) Find the set of real-valued fundamental solutions and the real-valued general (c) Describe the behavior as t-o for each of the solutions in the fundamental set (d) Find a particular solution y(t) satisfying the given initial conditions. solution to the first-order system in part (a) of solutions. Hint: remember that u-y from your substitution in part (a).
Show transcribed image text 3. (3 points each) Consider the initial value problem y" -y" 3y +5y 0 with y(0) 0, y(0) 3, y"(0) 3. (a) Write the third-order differential equation as a system of first-order differential equations, i.e. write in the form uAu where u (ui, u2, uz)7 andy, (b) Find the set of real-valued fundamental solutions and the real-valued general (c) Describe the behavior as t-o for each of the solutions in the fundamental set (d) Find a particular solution y(t) satisfying the given initial conditions. solution to the first-order system in part (a) of solutions. Hint: remember that u-y from your substitution in part (a).