 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-1/11/a/ii/solution

e^{- x^{3} /3}

(y e^{- x^{3} /3})^{'} = x^{2} e^{- x^{3} /3} = - (e^{- x^{3} /3})^{'}

. Integrating gives

y (x) = C e^{x^{3} /3} - 1.

This includes the constant particular solution

y = - 1

when

C = 0

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