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Question
State whether the following statement is true or false.
The integrating factor of the differential equation `(dy)/(dx) + y/x` = x3 is – x.
Options
True
False
Solution
This statement is False.
Explanation:
`(dy)/(dx) + y/x` = x3
∴ `(dy)/(dx) + (x^-1). y = x^3`
Comparing with `(dy)/(dx) + Py = Q`, we get
P = x–1, Q = x3
Now, I.F. = `e^(intpdx)`
= `e^(intx^-1 dx)`
= `e^(logx)`
= x.
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