f-is-a-C-2-function-prove-that-1-L-f-x-L-f-f-0-2-L-f-x-2-L-f-xf-0-f-0-L-means-Laplace-transform-

Question Number 38457 by maxmathsup by imad last updated on 25/Jun/18

$${f}\:{is}\:{a}\:{C}^{\mathrm{2}} {function}\:\:{prove}\:{that}\: \\ $$$$\left.\mathrm{1}\right){L}\left({f}^{'} \right)={x}\:{L}\left({f}\right)−{f}\left(\mathrm{0}^{+} \right) \\ $$$$\left.\mathrm{2}\right){L}\left({f}^{''} \right)={x}^{\mathrm{2}} {L}\left({f}\right)\:−{xf}\left(\mathrm{0}^{+} \right)−{f}^{'} \left(\mathrm{0}^{+} \right) \\ $$$${L}\:{means}\:{Laplace}\:{transform}. \\ $$

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