This course is an introduction to techniques for solving differential equations with applications. Topics include definitions and terminology, initial value problems, differential equations as models, first order differential equations (separable equations, exact equations, linear equations using integrating factor, solutions by substitutions, systems of linear and nonlinear equations), second and higher order differential equations (homogenous and nonhomogeneous equations, reduction of order, homogenous linear equations with constant coefficients, undetermined coefficient, variation of parameters, Cauchy - Euler equation, systems of linear equations, nonlinear equations, spring/ mass systems, linear equations: boundary value problems), nonlinear equations - numerical solutions, power series solutions, solutions about ordinary points, solutions about singular points, Laplace transform, and applications of Laplace transforms with possible optional topics of step functions, discontinuous forcing functions, and impulse functions.