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Question
The integrating factor of the differential equation `dy/dx - y = x` is e−x.
Options
True
False
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Solution
This statement is True.
Explanation:
The given differential equation is:
`dy/dx - y = x`
This is a linear differential equation in the standard form:
`dy/dx + P(x)y = Q(x)`
Here, P(x) = −1, so the integrating factor (IF) is:
IF = `e^(int P(x) dx)`
= `e^(int -1 dx)`
= `e^(-x)`
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