Y_1 = e^4x is a solution to the following ode: y" - 2y' - 8y = 0. use reduction of order to find a 2nd linearly independent solution. step 1: let y = [select] then y' = [select] step 2: substitute y, y', and y" into the ode and simplify to get u" + 6u' = 0 step 3: reduce the order. let w = u'. step 4: solve the equation for w. w = c e^(-6x) step 5: solve for u. step 6. identify the two linearly independent solutions. y_1 = e^4x was given as one solution. a second linearly independent solution is y2 = e^(-2x)