Ejercicios de repaso sección 4.6

Evaluar las tranformadas

  1. L{tcos2t}\hspace{0.5cm} \mathscr{L}\left\{t{cos2t}\right\}

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

  3. L{t2senht}\hspace{0.5cm} \mathscr{L}\left\{t^2\mathrm{senht} \right\}

  4. L{t2cost}\hspace{0.5cm} \mathscr{L}\left\{t^2\mathrm{cost} \right\}

  5. L{te2tsen6t}\hspace{0.5cm} \mathscr{L}\left\{\mathrm{t}\mathrm{e}^{2t}\mathrm{sen6t} \right\}

  6. L{te−3tcos3t}\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. y′+y=tsent\hspace{0.5cm} y\prime+y=tsent sujeta a la condición y(0)=0y(0)=0

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

  9. y′′+9y=cos3t\hspace{0.5cm} y\prime\prime+9y=cos 3t sujeta a la condición y(0)=2    ∧    y´(0)=5y(0)=2 \;\; \wedge \;\; y´(0)=5

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