Thanks, though I already know the solution. I forgot to mention that in the first post.
The problem is I don't know how to come to that solution.
I want to solve it once so that I can have an idea how to come to that.
While trying to solve a problem in physics I got this system of 3, second order differential equations.
Solution should be equation for linear harmonic oscillator.
m\ddot{η}1+kη1-kη2=0
mn\ddot{η}2-kη1+2kη2-kη3=0
m\ddot{η}3-kη2+kη3=0
My attempts at the solution produced 6th order...
Thank you for your answer.
You explained it very nicely.
And the solution for that integral is arcussin(s).
But...
I tried substituting \frac{tan\varphi}{\sqrt{8}}=tan\theta but I didn't get desired result because I got this:
d\varphi=\frac{\sqrt{8}}{1-4cos^{2}\theta}d\theta
But I...
Hello.
I was trying to solve Lagrangian equation and I manage to reduce second order differential equation that I got:
\ddot{\varphi}+\alpha\frac{tan\varphi}{cos^{2}\varphi}=0;
where \alpha is a constant,
to first order differential equation:
\dot{\varphi}^{2}+...