Let y be a function of x. Which of the

The possible differential equations for the first order linear differential equation are:
${\displaystyle 1.y^{\prime }-x=y^2\sin \left(x\right)}$
${\displaystyle 2.y^{\prime }-x=y\sin \left(x\right)}$
${\displaystyle 3.{\left(y^{\prime }\right)}^2+y=\tan \left(2x\right)}$
${\displaystyle 4.y^{\prime }=y^2{e}^x}$
${\displaystyle 5.{\left(y^{\prime }\right)}^2+y=e^x}$
The general form of the first order linear differential equation is
${\displaystyle y^{\prime }+q\left(x\right)y=p\left(x\right)\dots \dots \left(1\right)}$
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
${\displaystyle y^{\prime }-x=y\sin \left(x\right)}$
Hence, option (b) is correct.