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Module 2: First-Order ODEs I

Learn the primary techniques for solving first-order ODEs analytically: separation of variables, integrating factors, exact equations, and substitution methods.

4 Lessons

~4-5 hours

10 Practice Problems

Module Quiz

Learning Objectives

Solve separable first-order ODEs by separation and integration
Apply integrating factors to solve first-order linear equations
Test for exactness and solve exact equations
Use Bernoulli and homogeneous substitutions to reduce nonlinear equations to linear/separable form

Module Lessons

1

Separable Equations

Rewrite dy/dx = g(x)h(y) and integrate each side independently.

2

First-Order Linear Equations and Integrating Factors

Solve y' + P(x)y = Q(x) using the integrating factor method.

3

Exact Equations

Identify and solve M dx + N dy = 0 when the exactness condition holds.

4

Substitution Methods: Bernoulli and Homogeneous

Transform nonlinear equations into solvable forms via clever substitutions.

After the Lessons

Practice Problems

10 problems covering all four solution techniques.

Module Quiz

10 questions to test your mastery.

Study Materials

Study Guide Quick Ref

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