Ejercicios de repaso sección 4.4

Evaluar las transformadas

  1. L{te10t}\hspace{0.5cm} \mathscr{L}\left\{te^{10t}\right\}
  2. L{te6t}\hspace{0.5cm} \mathscr{L}\left\{\mathrm{t}\mathrm{e}^{\mathrm{-6t}}\right\}
  3. L{t3e2t}\hspace{0.5cm} \mathscr{L}\left\{t^3e^{\mathrm{-2t}}\right\}
  4. L{t10e7t}\hspace{0.5cm} \mathscr{L}\left\{t^{10}e^{\mathrm{-7t}}\right\}
  5. L{t(et+e2t)2}\hspace{0.5cm} \mathscr{L}\left\{t\left(e^t+e^{\mathrm{2t}}\right)^2\right\}
  6. En los ejercicios 6 a 10, evalúe la transformada inversa

  7. L1{1(s+2)3}\hspace{0.5cm} \mathscr{L}^{-1}\left\{\dfrac{1}{\left(s+2\right)^3}\right\}
  8. L1{1(s1)4}\hspace{0.5cm} \mathscr{L}^{-1}\left\{\dfrac{1}{\left(s-1\right)^4}\right\}
  9. L1{1s26s+10}\hspace{0.5cm} \mathscr{L}^{-1}\left\{\dfrac{1}{s^2-6s+10}\right\}
  10. L1{1s2+2s+5}\hspace{0.5cm} \mathscr{L}^{-1}\left\{\dfrac{1}{s^2+2s+5}\right\}
  11. L1{ss2+4s+5}\hspace{0.5cm} \mathscr{L}^{-1}\left\{\dfrac{s}{s^2+4s+5}\right\}
  12. En los ejercicios 11 a 15, resolver el PVI

  13. y+4y=e4t\hspace{0.5cm} y'+4y=e^{-4t} sujeta a la condición y(0)=2y(0)=2
  14. yy=1+tet\hspace{0.5cm} y'-y=1+te^t sujeta a la condición y(0)=0y(0)=0
  15. y+2y+y=0\hspace{0.5cm} y''+2y'+y=0 sujeta a la condición y(0)=1        y´(0)=1y(0)=1 \;\; \wedge \;\; y´(0)=1
  16. y4y+4y=t3e2t\hspace{0.5cm} y''-4y'+4y=t^3e^{2t} sujeta a la condición y(0)=0        y´(0)=0y(0)=0 \;\; \wedge \;\; y´(0)=0
  17. y6y+9y=t\hspace{0.5cm} y''-6y'+9y=t sujeta a la condición y(0)=0        y´(0)=1y(0)=0 \;\; \wedge \;\; y´(0)=1