Number of inflection points for the curve $$\,\,\,y = x + 2{x^4}\,\,\,\,$$ is_______.

The function $$f\left( x \right) = {e^x}$$ is _________.

For the function $$\phi = a{x^2}y - {y^3}$$ to represent the velocity potential of an ideal fluid, $${\nabla ^2}\,\,\phi $$ should be equal to zero. In that case, the value of $$'a'$$ has to be

If $$c$$ is a constant, then the solution of $${{dy} \over {dx}} = 1 + {y^2}$$ is