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The number of real zeros of the solution of a linear homogeneous differential equation

Published online by Cambridge University Press:  24 October 2008

M. N. Brearley
M. N. Brearley
Affiliation:
University of Adelaide, Australia
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Extract

The following theorem will be established:

Provided the roots of the associated characteristic equation are all real, any solution of a linear homogeneous differential equation with constant coefficients has at most n − 1 zeros for real finite values of the independent variable, where n is the order of the equation.

The theorem applies to equations with a complex independent variable, but since the conclusion concerns only real values of the variable there is no loss of generality in considering an equation of order n in the form

with y = y(x), where x is real. The constant coefficients ar may be complex.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 693 - 694
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

Forsyth, A. R.A treatise on differential equations (London, 1948).Google Scholar