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4.2.1. Homogeneous second order linear differential equations with constant coefficients

Lecture



The differential equation y "+ p · y '+ q · y = 0 , where p and q are constant, is called a homogeneous second-order linear equation.

The form of the general solution y 0 of a homogeneous second-order linear equation depends on the roots k 1 , k 2 of the characteristic equation:

  4.2.1.  Homogeneous second order linear differential equations with constant coefficients .
  1. If k 1 , k 2 are real numbers, and k 1k 2 , then the general solution is:   4.2.1.  Homogeneous second order linear differential equations with constant coefficients
  2. If k 1 , k 2 are real numbers, and k 1 = k 2 , then the general solution will be:   4.2.1.  Homogeneous second order linear differential equations with constant coefficients .
  3. If k 1 , k 2 are complex numbers,   4.2.1.  Homogeneous second order linear differential equations with constant coefficients where   4.2.1.  Homogeneous second order linear differential equations with constant coefficients , then the general solution is:   4.2.1.  Homogeneous second order linear differential equations with constant coefficients

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Mathematical analysis. Differential equations

Terms: Mathematical analysis. Differential equations