 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2019-resit/10/c/solution

The operator is

(D + 1)^{2}

y = e^{- x} u

; direct differentiation gives

(D + 1)^{2} y = e^{- x} u^{''}

. Hence

u^{''} = 3 x^{2}

, and two integrations give

y = e^{- x} (\frac{x ^{4}}{4} + C_{1} x + C_{2}) .

e^{- x}

and

x e^{- x}

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