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Question
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.
Options
x
logx
`1/x`
– x
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Solution
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is `1/x`.
Explanation:
The given differential equation is `x ("d"y)/("d"x) - y = x^4 - 3x`
⇒ `("d"y)/("d"x) - y/x = x^3 - 3`
Here, P = `- 1/x` and Q = `x^3 - 3`
So, integrating factor = `"e"^(int Pdx)`
= `"e"^(int 1/x "d"x)`
= `"e"^(-logx)`
= `"e"^(log 1/x)`
= `1/x`.
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