SEPARABLE DIFFERENTIAL EQUATION

In Problems 1–22 solve the given differential equation by separation
of variables.

1. dy = sin 5x dx
2. dy = (x + 1)2 dx
3. dx + 23«ily = 0 dy 5. x 4. dy

Differential Equations with Boundary-Value Problem by Zill

📘 Separable Differential Equations | Complete Step-by-Step Tutorial with Examples

Welcome to this comprehensive tutorial on separable differential equations, a fundamental technique used to solve first-order differential equations in calculus and applied mathematics. This method is essential for students in engineering, physics, computer science, and any discipline that involves mathematical modeling.

In this video, we take a deep dive into what separable differential equations are and how to solve them from start to finish using a clear, structured approach. We'll guide you through the entire process—from identifying separability to solving the equation and applying initial conditions.

📚 What You’ll Learn in This Tutorial:

What it means for a differential equation to be "separable"

How to rearrange terms to isolate variables on each side of the equation

Proper integration techniques to solve both sides

How to solve for the general solution and simplify your result

How to apply an initial condition (if given) to find a particular solution

Common mistakes to avoid when solving separable differential equations

Real-world examples where separable differential equations are used (e.g., population growth, cooling, and motion)

🧠 Example Problems Covered:

Basic separable equations with polynomial and exponential terms

A problem with an initial condition (IVP)

A real-life word problem modeled by a separable differential equation

Whether you're a calculus student, an engineering major, or simply reviewing for an exam, this video is designed to give you the clarity and confidence you need to master this technique.

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Видео SEPARABLE DIFFERENTIAL EQUATION канала Ardi Satriawan