Question:
For a ∈ (−2π, 0), consider the differential equation
\(x^2\frac{d^2y}{dx^2}+ax\frac{dy}{dx}+y=0\) for x > 0.
Let D be the set of all a ∈ (−2π, 0) for which all corresponding real solutions to the above differential equation approach zero as x → 0+. Then, the number of elements in D ∩ \(\Z\) equals ___________
For a ∈ (−2π, 0), consider the differential equation
\(x^2\frac{d^2y}{dx^2}+ax\frac{dy}{dx}+y=0\) for x > 0.
Let D be the set of all a ∈ (−2π, 0) for which all corresponding real solutions to the above differential equation approach zero as x → 0+. Then, the number of elements in D ∩ \(\Z\) equals ___________
\(x^2\frac{d^2y}{dx^2}+ax\frac{dy}{dx}+y=0\) for x > 0.
Let D be the set of all a ∈ (−2π, 0) for which all corresponding real solutions to the above differential equation approach zero as x → 0+. Then, the number of elements in D ∩ \(\Z\) equals ___________
Updated On: Oct 1, 2024
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Correct Answer: 6
Solution and Explanation
The correct answer is 6.
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