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(1) The order of ODE: the order of the highest derivative e.g.,

Chapter 14 First-order ordinary differential equation. (1) The order of ODE: the order of the highest derivative e.g.,. (2) The degree of ODE: After the equation has been rationalized, the power of the highest-order derivative. e.g.,.

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(1) The order of ODE: the order of the highest derivative e.g.,

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  1. Chapter 14 First-order ordinary differential equation (1) The order of ODE: the order of the highest derivative e.g., (2) The degree of ODE: After the equation has been rationalized, the power of the highest-order derivative. e.g., (3) The general solution of ODE contains constants of integration, that may be determined by the boundary condition. (4) Particular solution: The general solution contains the constants which are found by the boundary condition. (5) Singular solution: Solutions contain no arbitrary constants and cannot be found from the general solution.

  2. Chapter 14 First-order ordinary differential equation 14.1 General form of solution with n parameters satisfies an nth-order ODE in general. The boundary conditions on the solutions determine the parameters. Ex: Consider the group of functions

  3. Chapter 14 First-order ordinary differential equation 14.2 First-degree first-order equation • Separable-variable equation

  4. Chapter 14 First-order ordinary differential equation • Exact equations

  5. Chapter 14 First-order ordinary differential equation

  6. Chapter 14 First-order ordinary differential equation • Inexact equations: integrating factors

  7. Chapter 14 First-order ordinary differential equation

  8. Chapter 14 First-order ordinary differential equation • Linear equations

  9. Chapter 14 First-order ordinary differential equation

  10. Chapter 14 First-order ordinary differential equation • Homogeneous equations

  11. Chapter 14 First-order ordinary differential equation

  12. Chapter 14 First-order ordinary differential equation • Isobaric equations

  13. Chapter 14 First-order ordinary differential equation • Bernoulli’s equation

  14. Chapter 14 First-order ordinary differential equation

  15. Chapter 14 First-order ordinary differential equation • Miscellaneous equations

  16. Chapter 14 First-order ordinary differential equation

  17. Chapter 14 First-order ordinary differential equation 14.3 Higher-degree first-order equation

  18. Chapter 14 First-order ordinary differential equation

  19. Chapter 14 First-order ordinary differential equation

  20. Chapter 14 First-order ordinary differential equation • Clairaut’s equation

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