Chapter 9.2, Problem 1ED

(A)

To determine

To explain: Whether the differential equation $y^{\prime }=x^{2}y$ can be written in the form of $f\left(y\right)y^{\prime }=g\left(x\right)$ else explain the reason why it is not possible.

(B)

To determine

To explain: Whether the differential equation $y^{\prime }=x^2+xy$ can be written in the form of $f\left(y\right)y^{\prime }=g\left(x\right)$ else explain the reason why it is not possible.

(C)

To determine

To explain: Whether the differential equation $y^{\prime }=x^{2}y+xy$ can be written in the form of $f\left(y\right)y^{\prime }=g\left(x\right)$ else explain the reason why it is not possible.