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Question
Find the general solution of the differential equation `dy/dx - y = sin x`
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Solution
The given differential equation is
`dy/dx - y = sin x` .....(1)
Clearly, it is a linear differential equation of the form `dy/dx + Py=Q`
Here
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∴ I.F. = `"e"^(int-"d"x)` = e–x
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∴ ye–x = `2int x*"e"^-x "d"x + "c"`
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= `2{x ("e"^-x)/(-1) - int ("e"^-x)/(-1)*1"d"x} + "c"`
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