Respuestas - Capítulo 4

Aquí encontrarás las respuestas a todos los ejercicios del capítulo 4

  1. y(t)=52−2e3t−35e−t+1110e−4t\hspace{0.5cm} y(t)=\dfrac{5}{2}-2e^{3t}-\dfrac{3}{5}e^{-t}+\dfrac{11}{10}e^{-4t}

  2. y(t)=10cost+2sent−2sen2t\hspace{0.5cm} y(t)=10cos{t}+2sent-\sqrt2sen\sqrt2t

  3. y(t)=110et−130sen3t−110cos3t\hspace{0.5cm} y(t)=\dfrac{1}{10}e^t-\dfrac{1}{30}sen3t-\dfrac{1}{10}cos{3}t

  4. y(t)=34+98t+34t2+14t3+14e2t−138te2t\hspace{0.5cm} y(t)=\dfrac{3}{4}+\dfrac{9}{8}t+\dfrac{3}{4}t^2+\dfrac{1}{4}t^3+\dfrac{1}{4}e^{2t}-\dfrac{13}{8}te^{2t}

  5. y(t)=−32e3tsen2t\hspace{0.5cm} y(t)=-\dfrac{3}{2}e^{3t}sen2t

  6. y(t)=2e−5tcost2+102e−5tsent2\hspace{0.5cm} y(t)=2e^{-5t}cos{\dfrac{t}{\sqrt2}}+10\sqrt2e^{-5t}sen\dfrac{t}{\sqrt2}

  7. y(t)=12−12etcost+12etsent\hspace{0.5cm} y(t)=\dfrac{1}{2}-\dfrac{1}{2}e^tcos{t}+\dfrac{1}{2}e^tsent

  8. y(t)=725+15t−725etcos2t+5125etsen2t\hspace{0.5cm} y(t)=\dfrac{7}{25}+\dfrac{1}{5}t-\dfrac{7}{25}e^tcos{2}t+\dfrac{51}{25}e^tsen2t

  9. y(t)=1−e−t−2[1−e−(t−1)]μ(t−1)\hspace{0.5cm} y(t)=1-e^{-t}-2\left[1-e^{-\left(t-1\right)}\right]\mu\left(t-1\right)

  10. y(t)=−14+12t+14e−2t−[14+12(t−1)−14e−2(t−1)]μ(t−1)\hspace{0.5cm} y(t)=-\dfrac{1}{4}+\dfrac{1}{2}t+\dfrac{1}{4}e^{-2t}-\left[\dfrac{1}{4}+\dfrac{1}{2}\left(t-1\right)-\dfrac{1}{4}e^{-2\left(t-1\right)}\right]\mu\left(t-1\right)

  11. y(t)=[16−12e2(t−1)+13e3(t−1)]μ(t−1)+e3t−e2t\hspace{0.5cm} y(t)=\left[\dfrac{1}{6}-\dfrac{1}{2}e^{2\left(t-1\right)}+\dfrac{1}{3}e^{3\left(t-1\right)}\right]\mu\left(t-1\right)+e^{3t}-e^{2t}

  12. y(t)=[1−cos(t−π)]μ(t−π)−[1−cos(t−2π)]μ(t−2π)+sent\hspace{0.5cm} y(t)=\left[1-cos{\left(t-\pi\right)}\right]\mu\left(t-\pi\right)-\left[1-cos{\left(t-2\pi\right)}\right]\mu\left(t-2\pi\right)+sent