A First Course in Differential Equations with Modeling Applications notes

Laplace Transformation Sufficient Conditions for Existence of Laplace Transformation Inverse Laplace Transformation Termwise Division Solving Linear Ordinary Differential Equations Solving an Initial Value Problem using Laplace Transformation Second Translation Theorem

Linear Systems, Eigen Values and Eigen Vectors Matrix Form of a Linear System Super Position Principle of Homogeneous Systems Criterion for Linear Independent Systems Existence of Fundamental Set of Solutions

Derivative of Laplace Transforms Transform of a Periodic Function Unit Impulse Transform of Dirac Delta Function Coupled Spring and Double Pendulum Problem

This is page one of a front and back study guide for an exam on second order differential equations. The topics included between the two pages are linear independence, homogeneous linear equations, non-homogeneous linear equations, Cauchy-Euler equations, Laplace theorem, and word problem applications. Examples are included on the sheet. This sheet helped me very much with my exam, hopefully it can help you just has much. I got an 87% on a very hard exam.