1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ln(y) and exp(y) :S

  1. Nov 30, 2009 #1
    Ive got the equation: sin(x) = ln(y) + (y^2)/2 + k

    The k is a constant from an earlier integration. How do I isolate y? What makes it hard for me is that if i want to get rid of ln() i need to use exp() but then the other y is in exp() and if i want to get rid of that, the first y is in ln() again.

    Sorry, for the bad english =) I hope you can help.
     
  2. jcsd
  3. Nov 30, 2009 #2

    Mentallic

    User Avatar
    Homework Helper

    I'm afraid it's not possible to isolate y algebraically.

    Taking the exponential of both sides: [tex]y=e^{sinx-\frac{y^2}{2}-k}=\frac{e^{sinx-k}}{e^{\frac{y^2}{2}}}[/tex]

    So now you have: [tex]ye^{\frac{y^2}{2}}=e^{sinx-k}[/tex]

    There is some method to solving for x in: [itex]xe^x=y[/itex]
    but the name of it has slipped my mind and whether it can be adapted to solve for y in your problem I'm unsure of as well. Hopefully someone else can help you with this.
     
  4. Nov 30, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Generally speaking, when you have a variable both "inside" and "outside" a transcendental function, there is no algebraic way to isolate that variable.

    The "method of solving [itex]xe^x= y[/itex]" is "Lambert's W function" which is defined as the inverse function to [itex]xe^x[/itex]. That is, [itex]W(xe^x)= x[/itex] so [itex]W(xe^x)= W(y)[/itex] and [itex]x= W(y)[/itex].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Ln(y) and exp(y) :S
  1. Solving for y (Replies: 3)

  2. Find y (Replies: 2)

  3. Solving for y (Replies: 6)

  4. Is it y-intercept? (Replies: 4)

Loading...