The following differential equation has $$3{{{d^2}y} \over {d{t^2}}} + 4{\left( {{{dy} \over {dt}}} \right)^3} + {y^2} + 2 = x$$

A solution of the differential equation $${{{d^2}y} \over {d{x^2}}} - 5{{dy} \over {dx}} + 6y = 0\,$$ is given by

$$y = {e^{ - 2x}}$$ is a solution of the differential equation $$\,{y^{11}} + {y^1} - 2y = 0$$