Ordinary Differential Equation

What you’ll study

Ordinary differential equations and their solutions: classification of differential equations, implicit and singular solutions, initial- and boundary-value problems, basic existence and uniqueness theorems, direction fields and the phase line. Solution of first-order equations: separable equations, linear equations, exact equations, special integrating factors, substitutions and transformations; modelling with first-order equations — exponential growth and decay, heating and cooling, mixtures, series circuits, logistic growth, chemical reactions, falling bodies; orthogonal and oblique trajectories. Higher-order linear differential equations: linear differential operators, homogeneous and non-homogeneous equations, reduction of order, the method of undetermined coefficients, variation of parameters, Euler-Cauchy equations. Modelling with second-order equations: vibration of a mass on a spring — free, damped and forced motion, resonance, electrical problems.