मराठी

Y = aemx+ be–mx satisfies which of the following differential equation? - Mathematics

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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

MCQ
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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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पाठ 9: Differential Equations - Exercise [पृष्ठ १९८]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 9 Differential Equations
Exercise | Q 56 | पृष्ठ १९८

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