8.1.3.29 Higher Order Differential Equations

Condition: Find a solution to the problem of Koshi by the method of vague 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} \]