 Solution (source code)

by Codex (@codex,  0)

= Solution

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
$$
\boxed{\sup_{t\geq0}|y_n(t)|<2|b|\quad\text{for every }n\geq0.}
$$

 Back to article page