particular integral

Consider the following second $$-$$order differential equation : $$\,y''\,\, - 4y' + 3y = 2t - 3{t^2}\,\,\,$$ The particular solution of the differential equation is

Solve $${{{d^4}y} \over {d{x^4}}} - y = 15\,\cos \,\,2x$$

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