Asymptotic representation of the solutions of linear differential equations when the characteristic equation has multiple roots

1977 ◽  
Vol 29 (2) ◽  
pp. 188-192 ◽  
Author(s):  
V. K. Grigorenko
Keyword(s):  
Differential Equations ◽  
Characteristic Equation ◽  
Asymptotic Representation ◽  
Linear Differential Equations ◽  
Multiple Roots ◽  
Linear Differential

scholarly journals Inequalities for solutions of linear differential equations a contribution to the theory of servomechanisms

1952 ◽  
Vol 38 ◽  
pp. 13-16 ◽  
Author(s):  
Hans Bückner
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Characteristic Equation ◽  
Real Function ◽  
Order Differential Equation ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Image Position ◽  
Imaginary Roots

Consider the nth order differential equationwhere the coefficients cv are real constants and f is a real function continuous in the interval a≦ x ≦ b. The following theorem will be proved in §4:If the characteristic equation of (I) has no purely imaginary roots, then a particular integral η (x) can always be found which satisfies the inequalitywhere C is a certain function of the cv only and M is the maximum of |f|. In particular we may take C = 1 if all roots of the characteristic equation are real.

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