The solution of the differential equation (x+2y3)dydx=y is

ydydx=x+2y3⇒dydx−xy=2y2 IF=e∫−1ydy=e−logy=1ySol is x(1y)=∫2y2ydy=y2+c x=y3+cy

The solution of the differential equation (x+2y3)dydx=y is

ydydx=x+2y3⇒dydx−xy=2y2 IF=e∫−1ydy=e−logy=1ySol is x(1y)=∫2y2ydy=y2+c x=y3+cy

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The solution of the differential equation $(x + 2 y^{3}) \frac{d y}{d x} = y$ is

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$x = y^{3} + c$

$x = y^{3} + c y$

$y = x^{3} + c$

$y = x^{3} + c x + d$

answer is B.

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Detailed Solution

$y \frac{d y}{d x} = x + 2 y^{3} \Rightarrow \frac{d y}{d x} - \frac{x}{y} = 2 y^{2}$
$I F = e^{\int - \frac{1}{y} d y} = e^{- \log y} = \frac{1}{y}$
Sol is $x (\frac{1}{y}) = \int \frac{2 y^{2}}{y} d y = y^{2} + c$
$x = y^{3} + c y$

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The solution of the differential equation $(x + 2 y^{3}) \frac{d y}{d x} = y$ is