First determine if the equation is exact. If it is exact, find the general solution, or at least a relation that defines the solutions implicitly:
[cos(x^2 + y) - 3xy^2]y' + 2x cos(x^2 + y) - y^3=0
To find whether it is exact or not we shall rewrite it as:
[cos(x^2 + y) - 3xy^2]dy+[2x cos(x^2 + y) - y^3]dx=0
p(x,y)=2x cos(x^2 + y) - y^3
Q(x,y)=cos(x^2 + y) - 3xy^2
The derivative of P wrt y would ...
This shows how to find if an equation is exact. The implicit differentiation is provided.