Maharashtra State BoardHSC Arts 12th Board Exam
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Solve the Differential Equation: - Mathematics and Statistics

Sum

 Solve the differential equation:

`("x" + "y") "dy"/"dx" = 1`

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Solution

`("x" + "y") "dy"/"dx" = 1`

`"dy"/"dx" = 1/("x" +"y") => "dx"/"dy" = "x" + "y"`

`"dx"/"dy" + (-1) "x" = "y"`

Comparing with `"dx"/"dy" + "P"."x" = "Q" "we get"`

P = -1 and Q = y

`therefore = "e"^(int-1"dy") = "e"^-"y"`

The general solution is 

x (IF) = ∫ Q (IF) dy +C

xe-y = y ∫ e-y dy +C

⇒ xe-y = -ye-y - e-y + C

⇒ (x + y + 1) = cey

Concept: Derivative - Revision of Derivative
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