If ey+xy=ex, then y2(0)= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

$e^{y} + x y = e^{x} \dots \dots (1)$

$x = 0 \Rightarrow e^{y} = 1 \Rightarrow y = 0$

differentiate with respect to $x$

$e^{y} . y^{1} + (y + x y^{1}) = e^{x} \dots \dots (2)$

$x = 0, y = 0$

$e^{0} . y^{1} (0) + (0 + 0) = e^{0} = 1$

$y^{1} (0) = 1$

$e^{y} . y^{11} + e^{y} . y^{1} . y^{1} + y^{1} + x y^{11} + y^{1} = e^{x}$ (differentiate with respect to $x$ in (2))

$put x = 0, y = 0, y^{1} (0) = 1$

$1. y^{11} (0) + e^{0} .1.1 + 1 + 0 + 1 = e^{0}$

$y^{11} (0) + 3 = 1$

$y^{11} (0) = - 2$

If $e^{y} + x y = e^{x}$ , then $y_{2} (0) =$