Show that the given general solution satisfies the given differential equation, showing all work carefully. Do NOT do this by solving the given differential equation, but rather prove that the whole general solution makes the equation true. DE= x^2y''- 8xy +8y=16
Gen. Sol y=c1x+c2x^8+2

Explanation:

Differentiating the solution, we have ...

  y' = c1 +8c2x^7

  y'' = 56c2x^6

Putting this into the DE, we have ...

  x^2y'' -8xy' +8y = 16 . . . . . . . different from your problem statement

  x^2(56c2x^6) -8x(c1 +8c2x^7) +8(c1x +c2x^8 +2) = 16

  56c2x^8 -8c1x -64c2x^8 +8c1x +8c2x^8 +16 = 16

  x^8(56c2 -64c2 +8c2) +x(-8c1 +8c1) +16 = 16

  0 +16 = 16 . . . . QED

answer: i think the answer is etheir c or d but i don't know which one but have a good day!

step-by-step explanation:

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: