ENGR 213 Lecture Notes - Lecture 4: Exact Differential, Integrating Factor, Ordinary Differential Equation

• School: Concordia University
• Department: Engineering
• Course: ENGR 213
• Professor: Georgios Vatistas

Document Summary

The differential expression is an exact differential in a region plane if it corresponds to the differential of some function f(x, y) It is an exact equation if the expression on the left side is an exact differential. 2. 4 exact equations, integrating factors1differential of a function of two variablesmethod of solutionintegrating factors. Given the equation of the form the equality holds. M(x, y) with respect to while holding x y constant f(x, y) = m(x, y)dx + g(y) Differentiate with respect to is the constant of integration. = y f(x, y) = n(x, y)dy + h(x) h (x) = 2. 4 exact equations, integrating factors22xydx + (x "2. Integrating these equations will give f(x, y) = x y +2. Take the partial derivative of the last expression with respect to and setting the result equal to. The solution of the equation in implicit form is. The solution of the equation in explicit form is.