The solution for the differential equation $$\,{{d\,y} \over {d\,x}} = {x^2}\,y$$ with the condition that $$y=1$$ at $$x=0$$ is

For what values of $$\alpha $$ and $$\beta $$ the following simultaneous equations have an infinite number of solutions $$$x+y+z=5,$$$ $$$x+3y+3z=9,$$$ $$$x + 2y + \alpha z = \beta $$$

The inverse of $$2 \times 2$$ matrix $$\left[ {\matrix{ 1 & 2 \cr 5 & 7 \cr } } \right]$$ is

The minimum and maximum eigen values of matrix $$\left[ {\matrix{ 1 & 1 & 3 \cr 1 & 5 & 1 \cr 3 & 1 & 1 \cr } } \right]$$ are $$-2$$ and $$6$$ respectively. What is the other eigen value?