Differential equations I

Other, , Prof. Chris Tisdell

Updated On 02 Feb, 19

Overview

Contents:
How to solve separable differential equations - Separable differential equations - How to solve initial value problems-Linear - first-order differential equations - First order, linear differential equation - Linear differential equations, first order - Homogeneous first order ordinary differential equation - How to solve ANY differential equation - Mixing problems and differential equations - How to solve 2nd order differential equations - Variation of parameters to solve differential equations - Variation of Constants / Parameters -Vibrating systems, ODEs + variation of parameters tutorial - Laplace transforms + differential equations

Fourier series + differential equations - Laplace transforms & differential equations - Differential equations: Laplace transforms - Heat equation: Separation of variables - Heat equation derivation - Wave equation: D'Alembert approach - Heat equation + Fourier series - How to solve linear differential equations - Heat equation + Fourier series + separation of variables - D'alembert's approach for boundary value problems - How to solve Chebyshev's equation - How to solve systems of ODEs without matrices - How to determine eigenvalues of a boundary value problem - Eigenvalues of a Sturm Liouville differential equation - Separable ODEs: an initial value problem - How to solve differential equations by substitution - D'alembert's approach for boundary value problems

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Lecture 15: Solution to a 2nd order, linear homogeneous ODE with repeated roots

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Lecture Details

Free ebook httptinyurl.comEngMathYTI discuss and solve a 2nd order ordinary differential equation that is linear, homogeneous and has constant coefficients. In particular, I solve$$y - 4y + 4y = 0.$$The solution method involves reducing the analysis to the roots of of a quadratic (the characteristic equation). Such an example is seen in 1st and 2nd year university mathematics.