Match each of the differential equations below with the correct category. If the differential equation belongs to more than one categories, the most specific category takes precedence. For example, a separable equation is also an exact equation but not vice versa. Hence, if the equation is both exact and separable, your answer should be separable. You should rewrite the equation equivalently by use of simple algebra such as factorizations and divisions and use the modified equation for classification. You may also rewrite the equation equivalently in a differential form such as Mdx+Ndy=0. A. x 2

yy ′

=sin(x)y 2

+1 B. y ′

+xy=2 lny

C. y ′

=(1+x+y+xy)e y

D. y ′′

+(y ′

) 2

=4y+x E. e y

+(2y+xe y

)y ′

=0 F. 2e y

+(2y+xe y

)y ′

=0 y ′

=(1+x+y+xy)e y

y ′′

+(y ′

) 2

=4y+x e y

+(2y+xe y

)y ′

=0 2e y

+(2y+xe y

)y ′

=0