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Separable Differential Equation

  1. Apr 15, 2008 #1
    1. The problem statement, all variables and given/known data

    dy/dx =[cos^2(x)][cos^2(y)]

    2. Relevant equations

    The solution to this problem is y = +/- [(2n + 1)*pi]/4

    How? Do i just plug C back into the equation? That seems a little messy

    3. The attempt at a solution

    dy/cos^2(y) = cos^2(x) dx

    After integrating: (1/2)tan(2y) = (1/2)(x + cos(x) + sin(x) + C)

    C = 2tan(2y) - 2x -sin(2x) for cos(2y) not = 0
  2. jcsd
  3. Apr 15, 2008 #2
    You have not supplied enough information to make your solution unique. What point must the curve pass through?
  4. Apr 15, 2008 #3


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    Science Advisor
    Homework Helper

    Hi aznkid310! :smile:

    No … you're getting your ^2 and your 2 mixed up … it's just tany on the left.

    And on the right … you've gone all weird! :rolleyes:

    Use cos²x = 1/2(1 + cos(2x)).
  5. Apr 16, 2008 #4
    It just saved solve the differential equation. But the solution included all of that.

    As for the integration, i checked w/ an integral calculator and the left side is correct. For the right side, its actually cos^2(2x), my mistake.
  6. Apr 16, 2008 #5

    D H

    Staff: Mentor

    Firstly, its [itex]y=\frac{2n+1}2\pi[/itex]. You don't need the [itex]\pm[/itex] and the denominator is 2, not 4.

    Secondly, this is not "the" solution. There are infinitely many solutions you can find via integrating the differential equation. Hint: You will not get these particular solutions by integrating the differential equation. Big hint: what is the derivative of [itex]y=c[/itex] with respect to [itex]x[/itex]?

    Thirdly, your integration ran afoul somewhere.
    Last edited: Apr 16, 2008
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