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

he general solution of the differential equation $${\log _e}\left( {{{dy} \over {dx}}} \right) = x + y$$ is