8.1.2.59 Second order differential equations

Condition: Find a particular solution to the differential equation in two ways. \[ \begin{array}{l} y^{\prime \prime}(t)-2 y^{\prime}(t)-35 y(t)=3 t-1 \\ y(0)=-3, \quad y^{\prime}(0)=-2 \end{array} \]