ENGR 213 Lecture Notes - Lecture 5: Homogeneous Function, Integrating Factor, Partial Fraction Decomposition

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

Document Summary

Homogeneous equations if a function number f then possesses the property f is said to be a homogeneous function of degree f(tx, ty) = t f(x, y) for some real. A first order differential equation in the form is said to be homogeneous if both coefficients homogeneous functions of the same degree. M(x, y) = x m(1, u) and n(x, y) = x n(1, u) where u = M(x, y) = y m(1, u) and n(x, y) = y n(1, u) where n = y x x y. Either the substitutions dependent variables, will reduce a homogeneous equation to a separable first-order differential equation are new y = ux x = vy where and u or v. M(x, y)dx + n(xy)dy = 0 can be rewritten as x m(1, u)dx + x n(1, u)dy = 0 u = or y = y x u x. Substituting the differential dy = udx + xdu.