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Differential Equations by E. Rukmangadachari

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3

Linear Differential Equations with Constant Coefficients

3.1 INTRODUCTION

In the previous chapter, we have studied the linear differential equation of the first order

 

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It is called a homogeneous (or reduced) equation if Q(x) ≡ 0 and a non-homogeneous equation if Q(x) ≢ 0.

If we substitute y = u + v in Eq. (3.1), we have

 

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which is satisfied if

 

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This shows that y = u + v is the general solution (or complete solution) of Eq. ...

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