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Chapter 3
Tables of problems based on basic differential equation types

3.1 First order ode
3.2 Second order linear ODE
3.3 Second order ode
3.4 Second ODE homogeneous ODE
3.5 Second ODE non-homogeneous ODE
3.6 Second order non-linear ODE
3.7 Solved using series method
3.8 Third and higher order ode
3.9 First order ode linear in derivative
3.10 System of differential equations
3.11 Third and higher order homogeneous ODE
3.12 Third and higher order linear ODE
3.13 Third and higher order non-linear ODE
3.14 First order ode non-linear in derivative
3.15 Higher order, non-linear and homogeneous
3.16 Higher order, non-linear and non-homogeneous
3.17 Second order, non-linear and homogeneous
3.18 Second order, non-linear and non-homogeneous
3.19 Third and higher order non-homogeneous ODE
3.20 Second or higher order ODE with constant coefficients
3.21 Higher order, Linear, Homogeneous and constant coefficients
3.22 Higher order, Linear, Homogeneous and non-constant coefficients
3.23 Higher order, Linear, non-homogeneous and constant coefficients
3.24 Second or higher order ODE with non-constant coefficients
3.25 Second order, Linear, Homogeneous and constant coefficients
3.26 Second order, Linear, Homogeneous and non-constant coefficients
3.27 Second order, Linear, non-homogeneous and constant coefficients
3.28 Higher order, Linear, non-homogeneous and non-constant coefficients
3.29 Second order, Linear, non-homogeneous and non-constant coefficients

This chapter shows how each CAS performed based on the following basic differential equations types. A differential equation is classified as one of the following types.

  1. First order ode.
  2. Second and higher order ode.

For first order ode, the following are the main classifications used.

  1. First order ode linear in \(y'(x)\).
  2. First order ode not linear in \(y'(x)\) (such as d’Alembert, Clairaut).

For second order and higher order ode’s, further classification is

  1. Linear ode.
  2. non-linear ode.

Another classification for second order and higher order ode’s is

  1. Constant coefficients ode.
  2. Varying coefficients ode

Another classification for second order and higher order ode’s is

  1. Homogeneous ode. (the right side is zero).
  2. Non-homogeneous ode. (the right side is not zero).

All of the above can be combined to give this classification

  1. First order ode.

    1. First order ode linear in \(y'(x)\).
    2. First order ode not linear in \(y'(x)\) (such as d’Alembert, Clairaut).

  2. Second and higher order ode

    1. Linear second order ode.

      1. Linear homogeneous ode. (the right side is zero).
      2. Linear homogeneous and constant coefficients ode.
      3. Linear homogeneous and non-constant coefficients ode.
      4. Linear non-homogeneous ode. (the right side is not zero).
      5. Linear non-homogeneous and constant coefficients ode.
      6. Linear non-homogeneous and non-constant coefficients ode.

    2. Nonlinear second order ode.

      1. Nonlinear homogeneous ode.
      2. Nonlinear non-homogeneous ode.

For system of differential equation the following classification is used.

  1. System of first order odes.

    1. Linear system of odes.
    2. non-linear system of odes.

  2. System of second order odes.

    1. Linear system of odes.
    2. non-linear system of odes.

Each table that follows shows the result per each ODE type.

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