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 ?
How to solve that ODE?
2
$\begingroup$
real-analysis
ordinary-differential-equations
1 Answers
3
Hint: Try separating variables.
-
0Ok, 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
-
0Try $u=a\cosh(z)$ – 2012-09-21
-
0You 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