First Order Homogeneous Ordinary Differential Equations 3 | How to Solve First Order Homogeneous ODE

In this video, you will learn the solution to First Order Homogeneous Ordinary Differential Equations by substituting y=vx. This video provides a step-by-step guide on how to solve fFirst Order Homogeneous Ordinary Differential Equations. If you need a proper guide to understanding how first order homogeneous differential equations works, then this video is for you.
Learn how to solve first order homogeneous ordinary differential equations easily and efficiently using the substitution y=vx! In this video, we'll break down the step-by-step process of using the substitution of the product of a function, y=vx to find the general solution to a First Order Homogeneous Ordinary Differential Equations. Whether you're a student struggling with calculus or a math enthusiast looking to improve your skills, this video is perfect for you. With clear explanations and examples, you'll be solving differential equations like a pro in no time! Learn how to solve First Order Homogeneous Ordinary Differential Equations!
This looks simple enough, but we find that we cannot express the RHS in the form of 'x-factors' and 'y-factors', so we cannot solve by the method of separating the variables.

In this case we make the substitution y = vx, where v is a function of x. So y = vx. Differentiate with respect to x (using the product rule): dy/dx = v+x(dv/dx)
then you substitute for y and dy/dx in the main equation thereby transforming the Equation in to separable type.

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