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Mathematical methods I course of the University of Oxford

Past exam of the mathematical methods I course of the University of Oxford

2014

The <first-order linear differential equation> has <integrating factor> $e^{\sin x}$. Multiplying through gives
$$
(ye^{\sin x})'=2\sin x\cos x\,e^{\sin x}.
$$
With $u=\sin x$, the right side integrates to $2e^u(u-1)$. Consequently
$$
\boxed{y=2\sin x-2+Ce^{-\sin x}.}
$$
All coefficients are smooth, so these real solutions extend over the whole real axis.

Solution

Past exam of the mathematical methods I course of the University of Oxford / 2014 / 9 / b / Solution

Past exam of the mathematical methods I course of the University of Oxford / 2014 / 9 / b / Solution

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Past exam of the mathematical methods I course of the University of Oxford / 2014 / 9 / b / Solution

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