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

Описание: 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
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