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प्रश्न
Solve the differential equation:
`"dy"/"dx" + "y" "sec" "x" = "tan""x"`
बेरीज
उत्तर
`"dy"/"dx" + "y" "sec" "x" = "tan""x"`
Comparing with `"dy"/"dx" +"P"."y" = "Q", "we get"`
P = sec x , Q = tan x
IF = `"e"^(int"P""dx") = "e"^(int "sec" "x" "dx") = "e"^("l""n"|"sec""x" + "tan""x")| = "sec""x" + "tan""x"`
therefore the general solution is
y(IF) = `int "Q"("IF") "dx" +"C"`
y(secx + tan x) = `int "tan x"("sec x" + "tanx")"dx" + "C"`
= `int("sec x tan x" + "tan"^2"x") "dx" +"C"`
`=int("sec x tan x" +"sec"^2"x" - 1) "dx" +"C"`
∴ y(sec x + tan x) = sec x + tan x - x +C
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