J-Man18

ED Lab 9

Nov 29th, 2019
521
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  1. https://rextester.com/l/octave_online_compiler
  2.  
  3. 1)
  4. y''' - 2 * y'' - 5 * y'
  5.  
  6. Rezolvare:
  7. 1)
  8.  
  9. pkg load symbolic
  10. syms y(x)
  11. dsolve(diff(y(x),3) - 2 * diff(y(x), 2) - 5*diff(y(x),x) + 6*y == exp(x) + x^2)
  12. syms r A0 A2 A1 y1(x) y2(x) y3(x) yp(x)
  13. solve(r^3 - 2*r^2 - 5*r + 6 == 0, r)
  14.  
  15. % y''' - 2y'' - 5y' + 6y = e^x
  16. %yp(x) = A0 * x * exp(x)
  17. %y1(x) = diff(yp(x), x)
  18. %y2(x) = diff(yp(x), 2)
  19. %y3(x) = diff(yp(x), 3)
  20.  
  21. %y3(x) - 2 * y2(x) - 5 * y1(x) + 6 * yp(x)
  22. %ec1 = simplify(y3(x) - 2 * y2(x) - 5 * y1(x) + 6 * yp(x))
  23.  
  24. % y''' - 2y'' - 5y' + 6y = x^2
  25.  
  26. yp(x) = A2 * x^2 + A1*x + A0
  27. y1(x) = diff(yp(x), x)
  28. y2(x) = diff(yp(x), 2)
  29. y3(x) = diff(yp(x), 3)
  30.  
  31. simplify(-4 * A2 - 5*(2*A2*x+A1) + 6*(A2*x^2 + A1*x +A0) == x^2)
  32. %mai era ceva cred
  33.  
  34. 2)
  35.  
  36. %syms y1(x) y2(x)
  37. %y1(x) = diff(y(x), x)
  38. %y2(x) = diff(y(x), 2)
  39. %dsolve(diff(y(x), 3) - 2* diff(y(x), 2) + 5 * diff(y(x), x) == - 24 * exp(3 * x), y(0) == 4, y1(0) == -1, y2(0) == -5)
  40.  
  41. %dsolve(diff(y(x), 3) - 3 * diff(y(x), 2) + 3 * diff(y(x), x) - y - exp(x) - sin(x))
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