Differential EquationHard

Question

Solution of differential equation  (1 + y2)dx + (x - etan-1y)dy = 0 is -

Options

A.yetan-1x = tan-1 x + c
B.xetan-1y = e2tan-1 + c
C.2x = etan-1y + c
D.y = xe-tan-1x + c

Solution

(1 + y2) + x = etan-1y

I.F. = etan-1y
Xetan-1y = dy
⇒  Xetan-1y = e2tan-1y + c

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