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The integrating factor of linear differential equation xdydx+2y=x2logx is ______. - Mathematics and Statistics

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प्रश्न

The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.

पर्याय

  • `1/"x"`

  • k

  • `1/"n"^2`

  • x2

  • x

  • `1/x^2`

MCQ
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उत्तर

The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is x2.

Explanation:

`x dy/dx + 2y = x^2 log x`

⇒ `dy/dx + (2/x)y = x log x`

This is Linear differential equation of the form

`dy/dx + P = Q`

where `P = 2/x`

∴ Integrating factor (I. F.) = `e^(int pdx)`

`e^(int 2/x dx)`

= `e^(2 log x)`

`e^(logx^2)`

= x2

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पाठ 6: Differential Equations - Miscellaneous exercise 1 [पृष्ठ २१६]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 6 Differential Equations
Miscellaneous exercise 1 | Q 1.1 | पृष्ठ २१६

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