Differential EquationHard

Question

Solution of differential equation (1 + y²)dx + (x - e^{tan^-1y})dy = 0 is -

Options

A.ye^{tan^-1x} = tan^-1 x + c

B.xe^{tan^-1y} = e^{2tan^-1} + c

C.2x = e^{tan^-1y} + c

D.y = xe^{-tan^-1x} + c

Solution

(1 + y²) + x = e^{tan^-1}y

I.F. = e^{tan^-1}y
Xe^{tan^-1y} = dy
⇒ Xe^{tan^-1y} = e^{2tan^-1y} + c

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