f-function-2-derivable-prove-that-L-f-pL-f-f-o-and-L-f-p-2-L-f-pf-0-f-0-2-let-f-t-tsin-wt-find-L-f-

Question Number 30477 by abdo imad last updated on 22/Feb/18

$${f}\:{function}\:\mathrm{2}\left(×\right)\:{derivable}\:{prove}\:{that} \\ $$$${L}\left({f}^{'} \right)=\:{pL}\left({f}\right)\:−{f}\left({o}\right)\:{and}\:{L}\left({f}^{''} \right)={p}^{\mathrm{2}} {L}\left({f}\right)−{pf}\left(\mathrm{0}\right)−{f}^{'} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{let}\:{f}\left({t}\right)={tsin}\left({wt}\right)\:{find}\:{L}\left({f}\right). \\ $$

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