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Differential equations 1 course of the University of Oxford

Past exam of the differential equations 1 course of the University of Oxford

2023

Put $B=|b|>0$ and $\gamma=4B/C_1<1$. Initially $M_0=B<2B$. If $M_n<2B$, the preceding <supremum norm> estimate gives
$$
M_{n+1}\leq B+\frac{M_n^2}{C_1}<B+\frac{4B^2}{C_1}=B(1+\gamma)<2B.
$$
Hence <mathematical induction> gives
$$
\boxed{\sup_{t\geq0}|y_n(t)|<2|b|\quad\text{for every }n\geq0.}
$$

Solution

Past exam of the differential equations 1 course of the University of Oxford / 2023 / 1 / b / ii / Solution

Past exam of the differential equations 1 course of the University of Oxford / 2023 / 1 / b / ii / Solution

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Past exam of the differential equations 1 course of the University of Oxford / 2023 / 1 / b / ii / Solution

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