Exact Equations
An exact equation is a type of differential equation that can be expressed in the form M(x, y)dx + N(x, y)dy = 0 , where the functions M and N are continuously differentiable. An equation is considered exact if the partial derivative of M with respect to y equals the partial derivative of N with respect to x . This property allows for the existence of a potential function F(x, y) such that dF = Mdx + Ndy .
To solve an exact equation, one typically finds the potential function F by integrating M with respect to x and N with respect to y . The solution to the equation is then given by the level curves of F , which represent the set of points where F(x, y) = C , with C