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Differential Equations by E. Rukmangadachari

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5

Linear Equation of the Second Order with Variable Coefficients

An equation of the form

 

image

 

where P, Q, R are the real valued functions of x defined on an interval I is called a linear equation of the second order with variable coefficients.

There is no known general method to solve such an equation. We discuss below three methods which are useful in the solution of second order linear equations with variable coefficients.

  1. Change of the dependent variable when part of the complementary function is known.
  2. Change of the dependent variable and removal of the first derivative or reduction to normal form.
  3. Change of the independent variable.

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