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Question
The Integrating Factor of the differential equation `dy/dx - y = 2x^2` is ______.
Options
e-x
e-y
`1/x`
x
Solution
The Integrating Factor of the differential equation `dy/dx - y = 2x^2` is `underline(1/x)`
Explanation:
The differential equation is
`x dy/dx - y = 2x^2`
or `dy/dx - 1/x y = 2x`
Here `P = - 1/x, Q = 2x`
∴ `∫ P dx =int - 1/x` dx
=` - log x = log 1/x`
⇒ `I.F. = e^(int P dx)`
`= e^(log 1//x) = 1/x`
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