The general solution of the differential equation $$\,\,{{dy} \over {dx}} = {{1 + \cos 2y} \over {1 - \cos 2x}}\,\,$$ is

Consider the differential equation $$\,\,{{dx} \over {dt}} = 10 - 0.2\,x$$ with initial condition $$x(0)=1.$$ The response $$x(t)$$ for $$t > 0$$ is

If $$a$$ and $$b$$ are constants, the most general solution of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{{dx} \over {dt}} + x = 0$$ is

If the characteristic equation of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 2\alpha {{dy} \over {dx}} + y = 0\,\,$$ has two equal roots, then the values of $$\alpha $$ are