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Question
The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.
Options
`1/"x"`
k
`1/"n"^2`
x2
x
`1/x^2`
Solution
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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