Given that $$\mathop x\limits^{ \bullet \bullet } + 3x = 0$$ and $$x\left( 0 \right) = 1,\,\,\mathop x\limits^ \bullet \left( 0 \right) = 1,$$ What is $$x(1)$$ ________.

It is given that $$y'' + 2y' + y = 0,\,\,\,\,y\left( 0 \right) = 0,y\left( 1 \right) = 0.$$ What is $$y(0.5)$$?

A coin is tossed $$4$$ times. What is the probability of getting heads exactly $$3$$ times?

The divergence of the vector field $$\left( {x - y} \right)\widehat i + \left( {y - x} \right)\widehat j + \left( {x + y + z} \right)\widehat k$$ is