Solve $${{{d^4}v} \over {d{x^4}}} + 4{\lambda ^4}v = 1 + x + {x^2}$$

The solution of a differential equation $${y^{11}} + 3{y^1} + 2y = 0$$ is of the form

The differential equation $${{{d^4}y} \over {d{x^4}}} + P{{{d^2}y} \over {d{x^2}}} + ky = 0\,\,$$ is