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Math Help - Differentiate This

  1. #1
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    Differentiate This

    Hi

     \displaystyle y(1+x^2)y'-x(1=y^2)=0\\
     \displaystyle $$\frac{y}{1+y^2}$$dy=$$\frac{x}{1+x^2}$$dx
     \displaystyle \int\frac{y}{1+y^2}dy =\int\frac{x}{1+x^2}dx
     \displaystyle \ln|1+y^2|^\frac{1}{2}=\ln|1+x^2|^\frac{1}{2}+C
    Stuck. I could use a hint as to how the constant C ends up with a natural log.

     \displaystyle Ans: 1+y^2=C(1+x^2)

    BTW: How does one indent to the next line without closing the line with [/tex] and repeating a new line with [tex]. Is there a shortcut to save time?
    Last edited by ugkwan; November 6th 2010 at 08:30 PM.
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  2. #2
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    Quote Originally Posted by ugkwan View Post
     \displaystyle \ln|1+y^2|^\frac{1}{2}=\ln|1+x^2|^\frac{1}{2}+C
    Stuck. I could use a hint as to how the constant C ends up with a natural log.
    You can say C = \ln{c} then add logs on the RHS.
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