8.1.3.29 Higher order differential equations

Condition: Find a solution to the Cauchy problem using the method of undetermined coefficients. \[ \begin{array}{l} y^{\prime \prime \prime}-2 y^{\prime \prime}+y^{\prime}=4 \\ y(0)=1, \quad y^{\prime}(0)=2, \quad y^{\prime \prime}(0)=-2 . \end{array}\]