The number of real zeros of the solution of a linear homogeneous differential equation
1961 ◽
Vol 57
(3)
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pp. 693-694
Keyword(s):
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 formwith y = y(x), where x is real. The constant coefficients ar may be complex.
2020 ◽
Vol 70
(2)
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pp. 53-58
1982 ◽
Vol 25
(4)
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pp. 435-440
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1986 ◽
Vol 9
(2)
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pp. 405-408
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1968 ◽
Vol 64
(3)
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pp. 721-730
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1949 ◽
Vol 62
(4)
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pp. 387-393
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Keyword(s):