 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2017-resit/10/a/solution

With

x = e^{t}

, the chain rule gives

x y^{'} = \overset{y}{˙}

and

x^{2} y^{''} = \overset{y}{¨} - \overset{y}{˙}

\overset{y}{¨} + 2 \overset{y}{˙} - 7 y = 0.

- 1 \pm 22

, so, in addition to the requested transformation, its general solution is

y (x) = C_{1} x^{- 1 + 22} + C_{2} x^{- 1 - 22}

x > 0

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