 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-2/3/solution

On an interval excluding

t = 0

t^{4}

. Multiplying through gives

\frac{d}{d t} (t^{4} y) = 3 t^{4} .

An antiderivative then gives

t^{4} y = 3 t^{5} /5 + C

, so

y (t) = \frac{3}{5} t + \frac{C}{t ^{4}}, t \neq = 0.

The constant is arbitrary on each connected interval of the domain; the original differential equation is undefined at zero.

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