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

Limit of the function, $$\mathop {Lim}\limits_{n \to \infty } {n \over {\sqrt {{n^2} + n} }}$$ is _______.

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