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For how many natural numbers m is y = e^(mx) a solution of the differential equation D³ y - 3 D² y - 4 D y + 12 y = 0 (where D = d/dx)?
- 0
- 1
- 2
- more than 2
Correct answer: 2
Solution
The characteristic equation factorises as (m-2)(m-3)(m+2) = 0, whose natural-number roots are 2 and 3.
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