(Solved): Consider the differential equation \[ y^{\prime \prime}-4 y^{\prime}+3 y=3 t \] (a) Find \( r_{1}, ...

Consider the differential equation \[ y^{\prime \prime}-4 y^{\prime}+3 y=3 t \] (a) Find \( r_{1}, r_{2} \), roots of the characteristic polynomial of the equation above. \[ r_{1}, r_{2}= \] (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. \[ \begin{array}{l} y_{1}(t)= \\ y_{2}(t)= \end{array} \] (c) Find a particular solution \( y_{p} \) of the differential equation above. \[ y_{p}(t)= \]