The solution to $$\,6y{y^1} - 25x = 0\,\,$$ represents a

The solution to $$\,\,{x^2}{y^{11}} + x{y^1} - y = 0\,\,$$ is

In numerical integration using Simpson's rule, the approximating function in the interval is a

In a vertical piston-cylinder arrangement the force applied to the piston, pushes water through a nozzle as shown in the figure. The water flows out from the nozzle, and reaches the top of its trajectory. The kinetic and pressure energies at points $$(1), (2)$$ and $$(3),$$ respectively, are