Consider the equation

1. Consider the equation :23\" + 2n? 6x = t2. (1) (a) (7 points) Show:r that 310:} = t2 and 32$) : r3 are independent solutions to the homogeneous equation :23" + 2n! {is = 0. That is, show each is a solution and showr the Wronslcian is nonzero. (b) (10 points) Solve (1) using variation of parameters. Hint: Don't forget to make the coefcient on the 2:" term one before jumping in. 2. Consider the initial value problem mu" +7u' +ku. = 0 \"(3) = \"a: \"'01) = vu- Assurne that we are in the critically damped case Where 72 : 4km. (a) (3 points) Show that if no matter the values of no and no, limb\