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First Order and Second Order Linear Differential Equations
Rating: 5.0 out of 5(6 ratings)
15 students

First Order and Second Order Linear Differential Equations

Diffrential Equations
Last updated 4/2025
English

What you'll learn

  • Solving first order ordinary differential equation using various methods
  • Solving second order differential equation
  • Operator method to solve second order differential equation and find particular solution
  • solving system of first order differential equations

Course content

3 sections56 lectures4h 33m total length
  • Introduction0:41
  • Definations4:43
  • Methods to solve ODE5:13
  • variable separable3:21
  • Special Question6:25
  • Picard's Theorem3:36
  • Homogeneous Equation6:46
  • Exact Equation5:40
  • specific Question4:44
  • Integrating Factor4:01
  • Z=xy type problem3:39
  • Summary+Formulas1:53
  • Imp Question3:02
  • Linear first Order Equation4:11
  • Practice Questions2:54
  • Bernoulli Eqn4:17
  • Z=logy case2:41
  • Reduction of order1:54
  • Problem on Reduction of Order3:04
  • Resource0:01

Requirements

  • Knowledge of basic calculus , like limits , derivatives , differentiation techniques , definite and indefinite integration

Description

Course Title: Methods to Solve First and Second Order Differential Equations & Systems of First-Order Equations

Differential equations play a fundamental role in mathematics, physics, engineering, and numerous real-world applications. This course is designed to provide a comprehensive understanding of first and second-order differential equations, covering various solution techniques essential for students, researchers, and professionals.

We begin with an introduction to first-order differential equations, exploring methods such as separation of variables, integrating factors, and exact equations.

Moving on to second-order differential equations, we delve into homogeneous and non-homogeneous cases. The course covers characteristic equations, the method of undetermined coefficients, and variation of parameters.

The final section of the course introduces systems of first-order differential equations, an essential topic for modelling complex dynamic systems.

Each module is structured with step-by-step explanations, worked-out examples, and problem-solving exercises to reinforce learning. By the end of the course, you will be equipped with analytical techniques to confidently solve first and second-order differential equations and apply them to various scientific and engineering disciplines.

Whether you're a student, engineer, or researcher, this course will help you confidently tackle differential equation problems and apply them to real-world scenarios.

Join us in mastering these essential mathematical tools and take your problem-solving skills to the next level!

Who this course is for:

  • All engineering disciplines
  • Bsc , MSc students
  • Statistics and data science
  • Finance and actuarial sciences