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General solution of differential equation: $(x+1) \large\frac{dy}{dx}$$-y = (x+1)^2$

$(a)\;\frac{y}{x+1}=(x+1)+y+c \\ (b)\;\frac{y}{x+1}=x+c \\ (c)\;\frac{x}{x+1}=y+c \\ (d)\;\frac{y}{x}=(x+1)+c $
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$\large\frac{dy}{dx}-\frac{y}{(x+1)} $$=x+1$
$I.F= e^{\int -\Large\frac{1}{x+1} dx}$
$\qquad= e^{- \log (x+1)}$
$\qquad= \large\frac{1}{x+1}$
$\large\frac{y}{x+1}=\int \large\frac{x+1}{x+1}$$dx+c$
$\large\frac{y}{x+1}$$=x+c$
Hence c is the correct answer.
answered Feb 4, 2014 by meena.p
 

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