Respuestas - Capítulo 4

Aquí encontrarás las respuestas a todos los ejercicios del capítulo 4

1. $\hspace{0.5cm} y(t)=\dfrac{5}{2}-2e^{3t}-\dfrac{3}{5}e^{-t}+\dfrac{11}{10}e^{-4t}$
2. $\hspace{0.5cm} y(t)=10cos{t}+2sent-\sqrt2sen\sqrt2t$
3. $\hspace{0.5cm} y(t)=\dfrac{1}{10}e^t-\dfrac{1}{30}sen3t-\dfrac{1}{10}cos{3}t$
4. $\hspace{0.5cm} y(t)=\dfrac{3}{4}+\dfrac{9}{8}t+\dfrac{3}{4}t^2+\dfrac{1}{4}t^3+\dfrac{1}{4}e^{2t}-\dfrac{13}{8}te^{2t}$
5. $\hspace{0.5cm} y(t)=-\dfrac{3}{2}e^{3t}sen2t$
6. $\hspace{0.5cm} y(t)=2e^{-5t}cos{\dfrac{t}{\sqrt2}}+10\sqrt2e^{-5t}sen\dfrac{t}{\sqrt2}$
7. $\hspace{0.5cm} y(t)=\dfrac{1}{2}-\dfrac{1}{2}e^tcos{t}+\dfrac{1}{2}e^tsent$
8. $\hspace{0.5cm} y(t)=\dfrac{7}{25}+\dfrac{1}{5}t-\dfrac{7}{25}e^tcos{2}t+\dfrac{51}{25}e^tsen2t$
9. $\hspace{0.5cm} y(t)=1-e^{-t}-2\left[1-e^{-\left(t-1\right)}\right]\mu\left(t-1\right)$
10. $\hspace{0.5cm} y(t)=-\dfrac{1}{4}+\dfrac{1}{2}t+\dfrac{1}{4}e^{-2t}-\left[\dfrac{1}{4}+\dfrac{1}{2}\left(t-1\right)-\dfrac{1}{4}e^{-2\left(t-1\right)}\right]\mu\left(t-1\right)$
11. $\hspace{0.5cm} y(t)=\left[\dfrac{1}{6}-\dfrac{1}{2}e^{2\left(t-1\right)}+\dfrac{1}{3}e^{3\left(t-1\right)}\right]\mu\left(t-1\right)+e^{3t}-e^{2t}$
12. $\hspace{0.5cm} y(t)=\left[1-cos{\left(t-\pi\right)}\right]\mu\left(t-\pi\right)-\left[1-cos{\left(t-2\pi\right)}\right]\mu\left(t-2\pi\right)+sent$