D Question 6 31=e-2 is a solution to the following ODE:"-2y-8y = 0. Use Reduction of Order to find a 2nd linearly independent solution. Step 1: Let y=[Select] [Select] Then y' [Sel ue^(-2x) e^(-2x) Step 2: Substitue^(-8x) simplify to get [Select] Step 3: Reduce e^(-8x) Step 4: Solve the equation for w. [Select] Step 5: Solve for u. Step 6. Identify the two linearly independent solutions. V₁ = e 3 was given as one solution. A second linearly independent solution is [Select] Question 6 31=e-2 is a solution to the following ODE:"-2-8y = 0. Use Reduction of Order to find a 2nd linearly independent solution. Step 1: Let y= [Select] Then y = [Select] [Select] u'e^(-8x) Step 2: Su E and simplify to get [Select] (u-2u)e^(-2x) Step 3: Re u'e^(-2x) Step 4: So (u-Bu)e^(-8x) Step 5: Solve for u. Step 6. Identify the two linearly independent solutions. V₁ = e 3c was given as one solution. A second linearly independent solution is [Select] D Question 6 31 = ez is a solution to the following ODE"-2y-8y = 0. Use Reduction of Order to find a 2nd linearly independent solution. Step 1: Let y= [Select] Theny= [Select] T Step 2: Substitute y, y, and y" into the ODE and simplify to get [Select] Step 3: Reduce the Order. Let w-u. Step 4: Solve the equation for w. [Select] Step 5: Solve for u. Step 6. Identify the two linearly independent solutions. 3 [Select] u"-2u'-0 u"-8u=0 u"-2u-8u=0 u"-6-0 = e was given as one solution. A second linearly independent sorUCIONES [Select] D Question 6 1=e-2 is a solution to the following ODE:" - 23-8y = 0. Use Reduction of Order to find a 2nd linearly independent solution. Step 1: Lety-[Select] Then y' [Select] = Step 2: Substitute y, y, and y" into the ODE and simplify to get [Select] Step 3: Reduce the Order. Let w-u. Step 4: Solve the equation for w. [Select] Step 5: Solve for u. [Select] Step 6. Identify the two linearly in dw/dx4w 20 ¼₁ = e was given as one solut dw/dx=8w [Select] w=6w w-2w ent solution is D Question 6 3/1 = e-2 is a solution to the following ODE"-2-8y=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 [Select] Step 3: Reduce the Order. Let w-u. Step 4: Solve the equation for w. [Select] Step 5: Solve for u. Step 6. Identify the two linearly independent solutions. -2x 3/1 = e was given as one solution. A second linearly independent solution is [Select] [Select] y2 =e^(2x) 12 XEM-2 y2 = e^(8x) y2 = e^(4x) y= 0, y(0)=4, 3 (0) = 4 10 pts