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I'm am trying to solve the following differentia equation $$ u'(x)=\frac{u(x)}{\sqrt{u^2(x)-\alpha^2}}, $$ where $\alpha$ is some non-zero real number. Any ideas ?

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Hint: Try separating variables.

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    Ok, if I understand correctly, I have to find a primitive $F(u)$ of $\sqrt{u^2-\alpha^2}/u$, and then to invert $F$, right ? But that looks hard to me !2012-09-21
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    Try $u=a\cosh(z)$2012-09-21
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    You may not be able to find an explicit expression for $x$ in terms of $t$; you may only be able to find an implicit relationship between the two.2012-09-21