Ejercicios de repaso sección 4.6

Evaluar las tranformadas

  1. $\hspace{0.5cm} \mathscr{L}\left\{t{cos2t}\right\}$

  2. $\hspace{0.5cm} \mathscr{L}\left\{\mathrm{tsenh3t}\right\}$

  3. $\hspace{0.5cm} \mathscr{L}\left\{t^2\mathrm{senht} \right\}$

  4. $\hspace{0.5cm} \mathscr{L}\left\{t^2\mathrm{cost} \right\}$

  5. $\hspace{0.5cm} \mathscr{L}\left\{\mathrm{t}\mathrm{e}^{2t}\mathrm{sen6t} \right\}$

  6. $\hspace{0.5cm} \mathscr{L}\left\{\mathrm{t}\mathrm{e}^{-3t}\mathrm{cos3t} \right\}$

    7. En los ejercicios 7 a 10 resolver el PVI

  7. $\hspace{0.5cm} y\prime+y=tsent$ sujeta a la condición $y(0)=0$

  8. $\hspace{0.5cm} y\prime-y=te^tsent$ sujeta a la condición $y(0)=0$

  9. $\hspace{0.5cm} y\prime\prime+9y=cos 3t$ sujeta a la condición $y(0)=2 \;\; \wedge \;\; y´(0)=5$

  10. $\hspace{0.5cm} y\prime\prime+y=sent$ sujeta a la condición $y(0)=1 \;\; \wedge \;\; y´(0)=-1$