# Let y be a function of x. Which of the

Let y be a function of x. Which of the following is a first order linear differential equation?
$1.{y}^{\prime }-x={y}^{2}\mathrm{sin}\left(x\right)$
$2.{y}^{\prime }-x=y\mathrm{sin}\left(x\right)$
$3.{\left({y}^{\prime }\right)}^{2}+y=\mathrm{tan}\left(2x\right)$
$4.{y}^{\prime }={y}^{2}{e}^{x}$
$5.{\left({y}^{\prime }\right)}^{2}+y={e}^{x}$
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Edward Patten
The possible differential equations for the first order linear differential equation are:
$1.{y}^{\prime }-x={y}^{2}\mathrm{sin}\left(x\right)$
$2.{y}^{\prime }-x=y\mathrm{sin}\left(x\right)$
$3.{\left({y}^{\prime }\right)}^{2}+y=\mathrm{tan}\left(2x\right)$
$4.{y}^{\prime }={y}^{2}{e}^{x}$
$5.{\left({y}^{\prime }\right)}^{2}+y={e}^{x}$
The general form of the first order linear differential equation is

The differential equations given in options (a), (c), (d) and (c) are not of the form as the differential equation given in equation (1).
So, the first order linear differential equation is given by
${y}^{\prime }-x=y\mathrm{sin}\left(x\right)$
Hence, option (b) is correct.
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