1. Not finding help here? Sign up for a free 30min 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!

Solving a Differential Equation

  1. Feb 6, 2011 #1
    1. The problem statement, all variables and given/known data

    Solve:
    2 * √(x) * (dy/dx) = cos^2(y)
    y(4) = π/4

    2. Relevant equations

    TRIGONOMETRIC RECIPROCAL IDENTITY: sec(u) = 1 / cos(u)
    arctan( 1 ) = π / 4

    3. The attempt at a solution

    This is a separable differential equation.

    2 * √(x) * (dy/dx) = cos^2(y)
    2 * √(x) * dy = cos^2(y) * dx
    [2 / cos^2(y)] * dy = [1 / √(x)] * dx
    TRIGONOMETRIC RECIPROCAL IDENTITY: sec(u) = 1 / cos(u)
    [2 * sec^2(y)] * dy = x^(-1/2) * dx

    ∫ [2 * sec^2(y)] * dy = ∫ x^(-1/2) * dx
    2 * tan(y) = 2 * √(x) + C
    y(x) = arctan( √(x) + C) <<< General Solution

    NOTE: arctan( 1 ) = π / 4
    y(4) = arctan( √(4) + C )
    y(4) = arctan( 2 + C)
    C = -1

    y(x) = arctan( √(x) - 1 ) <<< Particular Solution

    Is that all correct? Thank you!
     
  2. jcsd
  3. Feb 6, 2011 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper
    Insights Author

    Looks ok to me.
     
  4. Feb 6, 2011 #3
    Thanks! I just remembered that I can check these in my calculator as well.... >.<
     
  5. Feb 6, 2011 #4
    derivative y=√x+√x
    y'=?
     
  6. Feb 6, 2011 #5
    Um... what?

    Well, if
    y=√(x)+√(x)
    then
    y=2√(x)
    and
    y'=4x^(3/2)/3

    but you need to separate the variables first, then integrate not derive, so I don't see how that's relevant...?
     
  7. Feb 7, 2011 #6
    under sqrtx is also +sqrtx
     
  8. Feb 7, 2011 #7

    Char. Limit

    User Avatar
    Gold Member

    Don't hijack other problems with your own.
     
  9. Feb 7, 2011 #8
    sorry
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Solving a Differential Equation
Loading...