Using Convolution to Solve Differential Equations (Step-by-Step)

In this video, we use convolution to solve a differential equation step-by-step. We cover: • Setting up the ODE with Laplace transforms • Applying the convolution theorem • Writing the solution as a convolution integral • Interpreting the final result This shows how convolution is used to solve differential equations with more complicated inputs. 📘 Free guided notes are available here: https://www.understandthemath.com/ord... Classification    • Ordinary Differential Equations Full Cours...   First-Order Differential Equations    • How to Classify a Differential Equation (O...      • Slope Fields Explained Visually (Step-by-S...      • How to Solve Separable Differential Equati...      • Solving First-Order Linear ODEs with an In...      • How to Solve Exact Differential Equations      • How to Solve Homogeneous Differential Equa...      • How to Solve Bernoulli Differential Equations      • Modeling with First-Order Differential Equ...      • Euler’s Method Explained (Numerical Approx...      • Differential Equations Midterm Review | Fi...      • Logistic Growth Model Explained (Populatio...   Higher-Order Differential Equations    • How to Solve Second-Order Linear ODEs with...      • How to Find the Second Solution (Reduction...      • How to Use the Method of Undetermined Coef...      • Variation of Parameters Explained (Step-by...      • How to Solve Cauchy–Euler Differential Equ...   Modeling with First-Order Differential Equations    • How to Solve Mass–Spring Systems (Free Und...      • How to Solve Mass–Spring Systems (Free Dam...      • How to Solve Forced Mass–Spring Systems (D...      • Boundary Value Problem: Eigenvalues and Ei...      • How to Solve Forced Mass–Spring Systems (D...   Power Series Methods    • Power Series Method for Solving a Differen...      • Power Series Method for Solving Airy’s Equ...      • How to Identify Ordinary and Singular Poin...      • Method of Frobenius Example (Bessel’s Equa...   Laplace Transform Methods    • Laplace Transform Explained (Definition an...      • How to Compute Laplace Transforms (Using T...      • Laplace Transform of Derivatives (Step-by-...      • How to Find Inverse Laplace Transforms (St...      • How to Solve Differential Equations Using ...      • Unit Step Function, Translation Theorem, a...      • Convolution Integral and Convolution Theor...   Systems of Linear and Nonlinear First-Order Differential Equations    • Convert a Second-Order Differential Equati...      • Systems of Differential Equations (Eigenva...      • Finding and Classifying Critical Points of...      • Linearizing Nonlinear Systems Near Critica...   Connect & Support TikTok:   / understandthemath   Instagram:   / understandthemath   Facebook: https://www.facebook.com/profile.php?... Support: https://buymeacoffee.com/understandth... More About Understand The Math Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples. Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective. #ConvolutionODE #LaplaceTransform #DifferentialEquations #EngineeringMath #ODE #MathExamples #StepByStep