Inexact differential equation

An inexact differential equation is a differential equation of the form: M ( x , y ) d x + N ( x , y ) d y = 0 {\displaystyle M(x,y)\,dx+N(x,y)\,dy=0} satisfying the condition ∂ M ∂ y ≠ ∂ N ∂ x {\displaystyle {\frac {\partial M}{\partial y}}\neq {\frac {\partial N}{\partial x}}} Leonhard Euler invented the integrating factor in 1739 to solve these equations. == Solution method == To solve an inexact differential equation, it may be transformed into an exact differential equation by finding an integrating factor μ {\displaystyle \mu } .

Source: Wikipedia — Inexact differential equation (CC BY-SA 4.0)