Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.
(xy2 +x)dx + (y–x2y)dy=0
The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.
The above equation can be written as
x(
+1)dx=y(
–1)dy
–1)y=x(
+1)
=x
+x
So, from this equation it is clear that order of the differential equation is 1 and the degree of the differential equation is also 1.
In a differential equation, when the dependent variable and their derivatives are only multiplied by constants or independent variable, then the equation is linear.
So, in this question the dependent variable is y and the term 
is multiplied by y and also y is multiplied by itself, so the given equation is non-linear.