Question Number 92524 by naka3546 last updated on 07/May/20
$$\frac{{d}^{\mathrm{3}} {x}}{{dt}^{\mathrm{3}} }\:+\:\mathrm{27}\:\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }\:+\:\mathrm{243}\:\frac{{dx}}{{dt}}\:+\:\mathrm{729}{x}\:=\:{t}\centerdot\:{e}^{−\mathrm{9}{t}} \\ $$$$\:\:\:\:\:\:{x}\left(\mathrm{0}\right)\:=\:{x}'\left(\mathrm{0}\right)\:=\:{x}^{''} \left(\mathrm{0}\right)\:=\:\mathrm{0} \\ $$$${Use}\:\:{Laplace}\:\:{Transformation}\:\:{to}\:\:{solve}\:\:{it}\:. \\ $$