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Question
Choose the correct option from the given alternatives:
The solution of `"dy"/"dx" + "y" = cos "x" - sin "x"`
Options
yex = cos x + c
yex + ex cos x = c
yex = ex cos x + c
y2ex = ex cos x + c
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Solution
yex = ex cos x + c
Hint:
`"dy"/"dx" + "y" = cos "x" - sin "x"`
I.F. = `"e"^(int 1 "dx") = "e"^"x"`
∴ the solution is `"y" * "e"^"x" = int (cos "x" - sin "x")"e"^"x" + "c"`
∴ yex = ex cos x + c
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