Further Mathematics: How to identify & solve Homogeneous Differential Equation question(200L) скачать в хорошем качестве

Further Mathematics: How to identify & solve Homogeneous Differential Equation question(200L)

Welcome to Model Physics Mathematics Lessons. In this video, you will learn how to identify and solve a homogeneous differential equation using the substitution method. I begin by rewriting the equation into the standard first-order form: dy/dx = (xy-y^2)/(x^2+xy) Next, i test for homogeneity by examining the degree of each term: -x^2, xy, and y^2 are all degree 2. Since both numerator and denominator are homogeneous functions of the same degree, the equation is homogeneous. To solve it, i apply the standard substitution: y=vx, dy/dx = v + xdv/dx After substitution, the equation becomes separable, allowing us to integrate both sides and obtain the general solution. This method is commonly tested in WAEC, NECO, JAMB, and first-year university calculus, and this video explains it step by step for easy understanding. *What you'll learn: -How to identify a homogeneous differential equation -Meaning of degree in differential equations -Why substitution works -Step-by-step solution method -Common exam mistakes to avoid #goviral #homogeneousdifferentialequation #differentialequations #calculustutorial #waecmathematics #necomaths #jambmaths #UniversityCalculus #puremathematics #mathssimplified #ModelPhysicsAndMaths