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Question
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
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