MATH138 Study Guide - Midterm Guide: Ordinary Differential Equation, Dependent And Independent Variables
15 Sep 2018
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Intro to des, separable des, linear des, ivps. Definition: an equation containing derivatives of a dependent variable, =() is called an ordinary differential equation or ode. (there are also de"s for multivariable functions). Definition: the order of an ode is the order of the highest derivative that appears in the equation. + = sin 1-order cos( ) + = 1-order. Solution: sin , cos, multiplies of sin + cos. An ode is called linear if it contains only linear function in , , etc. (pretend is a constant): 3 + 23 = cos linear (pretend x3constant, 2 + = 0 linear, = linear. A particular solution is a solution in which all arbitrary constants have been determined. constants. Definition: the general solution of an ode id the set of all possible solutions, including arbitrary. An ode with initial condition is called an initial value problem.
