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प्रश्न
y = aemx+ be–mx satisfies which of the following differential equation?
पर्याय
`("d"y)/("d"x) + "m"y` = 0
`("d"y)/("d"x) - "m"y` = 0
`("d"^2y)/("d"x^2) - "m"^2y` = 0
`("d"^2y)/("d"x^2) + "m"^2y` = 0
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उत्तर
`("d"^2y)/("d"x^2) - "m"^2y` = 0
Explanation:
The given equation is y = `"ae"^("m"x) + "be"^(-"m"x)`
On differentiation, we get `("d"y)/("d"x) = "a" . "me"^("m"x) - "b" . "m"e^(-"m"x)`
Again differentiating w.r.t., we have
`("d"^2y)/("d"x^2) = "am"^2 "e"^("m"x) + "bm"^2 "e"^(-"m"x)`
⇒ `("d"^2y)/("d"x^2) = "m"^2 ("ae"^("m"x) + "be"^(-"m"x))`
⇒ `("d"^2y)/("d"x^2) = "m"^2y`
⇒ `("d"^2y)/("d"x^2) - "m"^2y` = 0
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