Proving 2nd Order Differential Eqns

  • Thread starter TannY
  • Start date
  • #1
2
0

Homework Statement


If y = (3x)/e^2x, find the value of x when d^2y/dx^2 = 0


Homework Equations


I'll just abbv d^2y/dx^2 as d2ydx2

The Attempt at a Solution


I kept getting stuck at:
d2ydx2 = 6/e^2
When d2ydx2 = 0,

6/e^2 = 0
6 = e^2

Then where's my x?? :confused: :confused:

P.S: i have serious issues with differentiation =.=
 

Answers and Replies

  • #2
30
0
y = 3x*e^(-2x)
y' = 3e^(-2x) - 6xe^(-2x)
y'' = -6e^(-2x) - 6e^(-2x) + 12xe^(-2x) = 0
-12e^(-2x) + 12xe^(-2x) = 0
12xe^(-2x) = 12e^(-2x)
x = 1

Differentiated using the chain rule (for exponentials) and product rule.
 
  • #3
2
0
thanx! ^^
i thought that (e^2x)squared = (e^4x) lol :biggrin:
 
  • #4
370
0
thanx! ^^
i thought that (e^2x)squared = (e^4x) lol :biggrin:
It is.

Filler Filler Filler.
 

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