QUESTION $1$

$(1\mathrm{.}1)$ Solve the system:

$x^{}+x+4y^{}=-6t^2$

$x^{}-x+y^{}-y=t^3-210$

by using the elimination method $($operator method$).$ Hint. Eliminate $y$ first.

$(1\mathrm{.}2)$ Just Reduce the system

$(8)$

$(D-1)[x]+D[y]=e^{2t}$

$2D[x]-4D[y]=2t^2$

to an equivalent triangular system of the form

$P_1[y]=f_1(t)$

$P_2[x]+P_3[y]=f_2(t)$

$[23]$