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CHAPTER 5 Higher-Order Linear Differntial Equations

CHAPTER 5 Higher-Order Linear Differntial Equations. Second-order DE:. (all). Second-order linear DE:. (a,c,d,e). Note: A,B,C,F function of x only. Second-order homogeneous linear DE:. Note: F(x)=0. (d,e). Second-order homogeneous linear DE (with constant coefficients):. (d).

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CHAPTER 5 Higher-Order Linear Differntial Equations

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  1. CHAPTER 5 Higher-Order Linear Differntial Equations Second-order DE: (all) Second-order linear DE: (a,c,d,e) Note: A,B,C,F function of x only Second-order homogeneous linear DE: Note: F(x)=0 (d,e) Second-order homogeneous linear DE (with constant coefficients): (d) Note: A, B, C, are constants

  2. CHAPTER 5 Higher-Order Linear Differntial Equations Second-order homogeneous linear DE: Note: F(x)=0 (d,e) are solutions ?? (verify) Consider the homogeneous 2ed-order linear DE: (*) Let W = the set of all solutions of (*) Let F = the set of all real-valued functions W is a subspace of F dim(W)=2

  3. CHAPTER 5 Higher-Order Linear Differntial Equations Second-order homogeneous linear DE: Consider the homogeneous 2ed-order linear DE: (*) W is a subspace of F dim(W)=2 Give me other solutions???

  4. CHAPTER 5 Higher-Order Linear Differntial Equations How to solve homog. 2ed-order linear DE: Consider the homogeneous 2ed-order linear DE: (*) 1 Find two linearly independent solutions for (*) 2 The general solution for (*)

  5. CHAPTER 5 Higher-Order Linear Differntial Equations How to y1 & y2: Consider the homogeneous 2ed-order linear DE (with constant coeff): (*) 1 Find the characteristic equation (**) 2 Find the roots of (**) Distinct real repeated real 2 non-real

  6. CHAPTER 5 Higher-Order Linear Differntial Equations How to y1 & y2: Consider the homogeneous 2ed-order linear DE (with constant coeff): (*) 1 Find the characteristic equation (**) 2 Find the roots of (**) Distinct real repeated real 2 non-real

  7. CHAPTER 5 Higher-Order Linear Differntial Equations How to y1 & y2: Consider the homogeneous 2ed-order linear DE (with constant coeff): (*) 1 Find the characteristic equation (**) 2 Find the roots of (**) Distinct real repeated real 2 non-real

  8. CHAPTER 5 Higher-Order Linear Differntial Equations How to solve homog. nth-order linear DE: Consider the homogeneous nth-order linear DE: (*) 1 Find n linearly independent solutions for (*) 2 The general solution for (*)

  9. How to y1, y2, .. yn: Consider the homogeneous nth-order linear DE (with constant coeff): 1 Find the characteristic equation (**) 2 Find the roots of (**) Distinct real repeated real non-real

  10. How to y1, y2, .. yn: Consider the homogeneous nth-order linear DE (with constant coeff): 1 Find the characteristic equation (**) 2 Find the roots of (**) Distinct real repeated real non-real

  11. CHAPTER 5 Higher-Order Linear Differntial Equations How to y1 & y2: Consider the homogeneous 2ed-order linear DE (with constant coeff): (*) 1 Find the characteristic equation (**) 2 Find the roots of (**) Distinct real repeated real 2 non-real

  12. How to y1, y2, .. yn: Consider the homogeneous nth-order linear DE (with constant coeff): 1 Find the characteristic equation (**) 2 Find the roots of (**) Distinct real repeated real non-real

  13. CHAPTER 5 Higher-Order Linear Differntial Equations Ploynomial Operator Write in operator form Euler’s Formula

  14. CHAPTER 5 Higher-Order Linear Differntial Equations How to solve homog. nth-order linear DE: Consider the homogeneous nth-order linear DE: (*) Find n linearly independent solutions for (*) 1 The general solution for (*) 2 How to solve non-homog. nth-order linear DE: Consider the non-homogeneous nth-order linear DE: (**) Solve the associated homog. DE (*) 1 (complementary function) 2 Find a particular solution for (**) 3 The general solution for (**)

  15. CHAPTER 5 Higher-Order Linear Differntial Equations How to solve homog. nth-order linear DE: Consider the non-homogeneous nth-order linear DE: (**) Solve the associated homog. DE (*) 1 (complementary function) 2 Find a particular solution for (**) 3 The general solution for (**)

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