ok so i have the differnetial equation

[latex] \lambda^{2} (\frac{dx}{dt})^{2} = (cos{ \alpha} - x)(cos{ \beta} - x) [/latex]

where [latex] x = cos{ \theta} [/latex]

and the solution is

[latex] x = cos{ \alpha} sin^{2}{\frac{t}{2 \lambda}} + cos{ \beta} cos^{2}{\frac{t}{2 \lambda}} [/latex]

please show you're working cos that's where im getting lost

now i want to use maple to show this is the solution to the eqn.

how do i do this???

also, if anybody can show me how to prove that is the solution to the equation using pen and paper that would be great too.

thanks for your help guys!