Maharashtra State BoardHSC Commerce 12th Board Exam
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Choose the correct alternative. The integrating factor of dydx-y=exis ex, then its solution is - Mathematics and Statistics

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MCQ

Choose the correct alternative.

The integrating factor of `dy/dx -  y = e^x `is ex, then its solution is

Options

  • ye −x = x + c

  • yex = x + c

  • yex = 2x + c

  • ye−x = 2x + c

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Solution

The integrating factor of `dy/dx -y = e^x `is ex, then its solution is ye −x = x + c

Explanation

`dy/dx -y = e^x`

Here, I.F. = e–x , Q = ex

∴ Solution of the given equation is

`y ( I.F.) = int Q ( I.F.) dx + c`

∴ `ye ^-x = int e^xe^-x dx+c`

∴ `ye ^-x = int 1dx + c`

∴ ye –x = x + c

Concept: Differential Equations
  Is there an error in this question or solution?
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 1.1 | Page 172
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