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Separable equations (but more like integration questions)

  1. Jun 15, 2005 #1
    Hi, I have just started my differential equations class. To solve the initial-value problem, 8cos^2ydx + csc^2xdy = 0 (initial condition: y(pai/12) = (pai/4) )using separable equations method, I have to change the equation to
    8/csc^2dx + 1/cos^2ydy (Am I right so far?)

    My problem is I don't know (or remember) how to integrate neither 8/csc^2dx nor 1/cos^2y. Am I suppose to do know how to calculate if I have finished Calculus II? I reviewed Trig. and Calculus textbooks to figure out how to calculate them but so far could not find even a similar problem.

    I also have no idea how to integrate the followings:

    a. x/secx dx
    b. 1/cot^2x dx
    c. 1/cos3y dx
    d. 1/sec^3 10x dx

    Any kind of help would be highly appreciated!
  2. jcsd
  3. Jun 15, 2005 #2
    The first one, you want to put the x's on one side and the y's on the other. To integrate sin^2 and secant squared you'll want to use some trig identities.

    [tex] \cos^2(x) = \frac{1}{2}(1+\cos(2x)) [/tex]. Others can be found here.

    a. xcosx dx, try parts.
    b. tan^2x, translate to secant.
    c. sec^3, translate sec^2 to tan^2+1
    d. trig identities.
  4. Jun 15, 2005 #3
    Thank you

    Thank you very much for the quick response.
    I will try to solve the problems with the reference you provided.
  5. Jun 15, 2005 #4
    Post again if you want a more thorough explanation.
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