Let k be a constant positive integer. Show that the nontrivial solutions of the equation dy dx2 +3(1+x)=0 have infinitely many zeros in (0,∞). Show also that the separation between adjacent zeros tends to zero as x → ∞.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let k be a constant positive integer. Show that the nontrivial solutions of
the equation
dy
dx2
+3(1+x)=0
have infinitely many zeros in (0,∞). Show also that the separation between
adjacent zeros tends to zero as x → ∞.
Transcribed Image Text:Let k be a constant positive integer. Show that the nontrivial solutions of the equation dy dx2 +3(1+x)=0 have infinitely many zeros in (0,∞). Show also that the separation between adjacent zeros tends to zero as x → ∞.
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