(1) The order of ODE: the order of the highest derivative

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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.
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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
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Chapter 14 First-order ordinary differential
equation
14.2 First-degree first-order equation

• Separable-variable equation

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Chapter 14 First-order ordinary differential
equation

• Exact equations

5
Chapter 14 First-order ordinary differential
equation
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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

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Chapter 14 First-order ordinary differential
equation
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Chapter 14 First-order ordinary differential
equation

• Isobaric equations

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Chapter 14 First-order ordinary differential
equation

• Bernoulli