Answer Happy

0 Question 7 = is a solution to the following ODE: "-21-8y=0. Use Reduction of Order to find a 2nd linearly independent solution. Complete each step of the Reduction of Order process necessary to find the general solution of the ODE. Step 1: Lety [Select] Then y'- [Select] Step 2: Substitute y. y. and y" into the ODE and simplify to get [Select] [Select] Step 3: Reduce the Order. Let wu u" - 2u²-0 Step 4: Solve the equation for w [Select] u"-6u = 0 Step 5: Solve for u. Step 6. Identify the two linearly independent solutions. U/₁ = e² was given as one solution. A second linearly independent solution is [Select] u-8u = 0 u" - 2u¹-8u = 0 8 pts
Step 2: Substitute y, y, and y" into the ODE and simplify to get [Select] Step 3: Reduce the Order. Let w = u'. [Select] [Select] w' = 2w dw/dx = 4w Y₁ = e 2 was given as one soluti w' = 6w dw/dx = 8w Step 4: Solve the equation for w'. Step 5: Solve for u. Step 6. Identify the two linearly ind ent solution is
Step 4: Solve the equation for W. Step 5: Solve for u. Step 6. Identify the two linearly independent solutions. Vi e was given as one solution. A second linearly independent solution is [Select] [Select] y2-e^(4x) y2 = e^(8x) y2=xeẠ(-2x) y2=e^(2x) Question 8 8 pt.