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)

no he doesnt because "-16' is negatiive

step-by-step explanation:

step-by-step explanation: 4 cause 2+2=4

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional