Solve this nonlinear differential equation
Hi, I'd like to solve the following differential equation to find 
as a function of 
(in fact I know what the answer should be due to the context, but I have no idea how to go about actually solving it). Any ideas would be appreciated!
^2 = \frac{y^2}{c^2})
,
where 
is a constant.
Re: Solve this nonlinear differential equation
Quote:
Originally Posted by
Amanda1990 
Hi, I'd like to solve the following differential equation to find
as a function of
(in fact I know what the answer should be due to the context, but I have no idea how to go about actually solving it). Any ideas would be appreciated!
,
where
is a constant.
^2 &= \frac{y^2}{c^2} \\ \left(\frac{dy}{dx}\right)^2 &= \frac{y^2}{c^2} - 1 \\ \left(\frac{dy}{dx}\right)^2 &= \frac{y^2 - c^2}{c^2} \\ \frac{dy}{dx} &= \frac{\pm\sqrt{y^2 - c^2}}{|c|} \\ \pm \frac{1}{\sqrt{y^2 - c^2}}\,\frac{dy}{dx} &= \frac{1}{|c|} \end{align*} )
You should now be able to solve this (it's separable).
Re: Solve this nonlinear differential equation
