Differential Equation

[prajendran]

Hi

I'm trying to solve this attached differential equation in mathcad... I'm running into an issue saying there is not enough initial conditions.

Please help with this issue. I was also unable to use laplace to solve this one too. By the way the F(t) is a periodic function from 0 to t5 where t5 is one of the unknowns and must be solved for.

Thanks

Prashanth Rajendran

[LucMeekes]

Like this?

Success!
Luc

[LucMeekes]

Some further elaboration:

Success!
Luc

[LucMeekes]

I assume that you want a real (not imaginary or complex) solution.

Note that for acos(x) it holds that the domain of x is [-1...1] and the resulting range of acos(x) is [0...pi].

With theta(t)=pi-acos(t), this means that the range of theta(t) is also [0...pi] and you will never find a theta value of 2*pi.

Your mathematical model (the original differential equation) is incorrect or (some of) your boundary conditions are impossible.

Please review both and correct where necessary before attempting to solve.

Success!
Luc

[prajendran]

The acos function gives to solutions. I believe that is the issue.

In that case, I have to include a new variable to set for theta(t)=pi, and if theta(t)<pi, use pi-acos(y(t)), if theta(t)>pi, use pi+acos(y(t))...