Ejercicios de repaso sección 3.5

Determinar la solución general de la ecuación diferencial

  1. y′′−10y′+25y=0\hspace{0.5cm} y^{\prime\prime}-10y^\prime+25y=0

  2. y′′+3y′=0\hspace{0.5cm} y^{\prime\prime}+3y^\prime=0

  3. 12y′′−5y′−2y=0\hspace{0.5cm} 12y^{\prime\prime}-5y^\prime-2y=0

  4. y′′+4y′−y=0\hspace{0.5cm} y^{\prime\prime}+4y^\prime-y=0

  5. 3y′′+y=0\hspace{0.5cm} 3y^{\prime\prime}+y=0

  6. y′′−4y′+5y=0\hspace{0.5cm} y^{\prime\prime}-4y^\prime+5y=0

  7. 2y′′−3y′+4y=0\hspace{0.5cm} 2y^{\prime\prime}-3y^\prime+4y=0

  8. y′′′−4y′′−5y′=0\hspace{0.5cm} y^{\prime\prime\prime}-4y^{\prime\prime}-5y^\prime=0

  9. y′′′−y′′−11y′+15y=0\hspace{0.5cm} y^{\prime\prime\prime}-y^{\prime\prime}-11y^\prime+15y=0

  10. y′′′−y′′−y′−2y=0\hspace{0.5cm} y^{\prime\prime\prime}-y^{\prime\prime}-y^\prime-2y=0

  11. y(4)−2y′′−3y′−2y=0\hspace{0.5cm} y^{\left(4\right)}-2y^{\prime\prime}-3y^\prime-2y=0

  12. 3y(4)−y′′′−21y′′−11y′+6y=0\hspace{0.5cm} 3y^{\left(4\right)}-y^{\prime\prime\prime}-21y^{\prime\prime}-11y^\prime+6y=0

  13. y(4)−8y′′′+14y′′+8y′−15y=0\hspace{0.5cm} y^{\left(4\right)}-8y^{\prime\prime\prime}+14y^{\prime\prime}+8y^\prime-15y=0

  14. y(4)+4y′′′+6y′′+4y′+y=0\hspace{0.5cm} y^{\left(4\right)}+4y^{\prime\prime\prime}+6y^{\prime\prime}+4y^\prime+y=0

  15. y(5)+5y(4)−2y′′′−10y′′+y′+5y=0\hspace{0.5cm} y^{\left(5\right)}+5y^{\left(4\right)}-2y^{\prime\prime\prime}-10y^{\prime\prime}+y^\prime+5y=0

  16. y′′−4y′−5y=0\hspace{0.5cm} y^{\prime\prime}-4y^\prime-5y=0 sujeta a y(1)=0∧y′(1)=2y\left(1\right)=0\land y^\prime\left(1\right)=2

  17. 4y′′−4y′−3y=0\hspace{0.5cm} 4y^{\prime\prime}-4y^\prime-3y=0 sujeta a y(0)=1∧y′(0)=5y\left(0\right)=1\land y^\prime\left(0\right)=5

  18. y′′+y′+2y=0\hspace{0.5cm} y^{\prime\prime}+y^\prime+2y=0 sujeta a y(0)=y′(0)=0y\left(0\right)=y^\prime\left(0\right)=0