Using Mathematica, solve the following differential equation by completing the following steps.

a$.$ Use DSolve to solve the following system.

b$.$ Use DSolve to solve the following system with conditions $x(0)=1,x^{\text{'}}(0)=0,y(0)=2.$

$x^{\text{'}}+y^{\text{'}}=t^2+t$

$x^{\text{'}\text{'}}+x+y=2t$

Please provide coding needed to answer problem and the results of these codes