The displacement x of a particle at time t is given by x = At² + Bt + C, where A, B, C are constants and v is velocity of a particle, then the value of 4Ax $$-$$ v² is

The displacement of a particle at time t is x, where x = t⁴ $$-$$ kt³. If the velocity of the particle at time t = 2 is minimum, then

The general solution of the differential equation $${{{d^2}y} \over {d{x^2}}} + 8{{dy} \over {dx}} + 16y = 0$$ is

The degree and order of the differential equation $$y = x{\left( {{{dy} \over {dx}}} \right)^2} + {\left( {{{dx} \over {dy}}} \right)^2}$$ are respectively