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  4. The solution of differential equation 2x (dy/dx) - y = 3 represents a family of

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Q. The solution of differential equation $2x \frac{dy}{dx} - y = 3$ represents a family of

BITSATBITSAT 2010

Solution:

We have,
$2 x \frac{d y}{d x}=y+3$
$\Rightarrow \frac{2}{y+3} d y=\frac{d x}{x}$
integrating, $2 \ln (y+3)$
$=\ln x+\ln c=\ln c x$
$\Rightarrow \ln (y+3)^{2}=\ln c x$
$\Rightarrow (y+3)^{2}=c x$
which is a family of parabolas.