$a.$ Find a particular solution $to$ the nonhomogeneous differential equation $y^{\text{'}\text{'}}+4y^{\text{'}}+5y=-10x+5e^{-x}.$

$y_p=$

$b.$ Find the most general solution $to$ the associated homogeneous differential equation. Use $c_1$ and $c_{2}in$ your answer

$to$ denote arbitrary constants, and enter them $asc1$ and $c2.$

$y_h=$

$c.$ Find the most general solution $to$ the original nonhomogeneous differential equation. Use $c_1$ and $c_{2}in$ your answer

$to$ denote arbitrary constants.

$y=(1)$