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General solution of differential equations: $\large\frac{dy}{dx}$$=e^{3x-2y}+x^2e^{-2y}$

$(a)\;3e^{2y}=2(e^{3x}+x^3)+c \\ (b)\;2e^{2y}=3(e^{3x}+x^3)+c \\ (c)\;3e^{2y}=2(e^{3x}-x^3)+c \\ (d)\;2e^{2y}=3(e^{3x}-x^3)+c $
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$\large\frac{dy}{dx}$$=e^{-2y} (e^{3x}+x^2)$
$\int e^{2y} dx= \int (e^{3x}+x^2)dx$
$\large\frac{e^{2y}}{2}=\frac{e^{3x}}{3}+ \frac{x^3}{3}+c$
$3e^{2y}=2(e^{3x}+x^3)+c$
Hence a is the correct answer.
answered Feb 4, 2014 by meena.p
 

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