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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Differential Equations

General solution of differential equation: $\large\frac{dy}{dx}$$=xe^{y-x^2}$

$(a)\;e^{-y^2}=2e^{-x} +c \\ (b)\;e^{-y}=2e^{-x^2} +c \\ (c)\;2e^{-y^2}=e^{-x^2} +c \\ (d)\;2e^{-y}=e^{-x^2} +c $

1 Answer

$\large\frac{dy}{dx}=\frac {xe^y}{e^{x^2}}$
$e^{-y} dy=xe^{-x^2}dx$
$\int e^{-y} = xe^{-x^2}dx$
$-x^2=t \qquad -2xdx=dt$
$+e^{-y}=+ \int e^t \large\frac{dt}{2}$$+c$
$e^{-y}=\large\frac{1}{2}e^t +c$
$2e^{-y}= e^{-x^2} +c$
Hence d is the correct answer.
answered Feb 4, 2014 by meena.p
 

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