For the differential equation $$\,\,{{dy} \over {dt}} + 5y = 0\,\,$$ with $$y(0)=1,$$ the general solution is

Solve for $$y$$ if $${{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0$$ with $$y(0)=1$$ and $${y^1}\left( 0 \right) = 2$$

If $$f(t)$$ is a finite and continuous Function for $$t \ge 0$$ the laplace transformation is given by
$$F = \int\limits_0^\infty {{e^{ - st}}\,\,f\left( t \right)dt,} $$ then for $$f(t)=cos$$ $$h$$ $$mt,$$ the laplace transformation is ___________.

A stone of mass m at the end of a string of length l is whirled in a vertical circle at a constant speed. The tension in the string will be maximum when the stone is