DFQ Term Paper Example | Topics and Well Written Essays - 750 words

DFQ - Term Paper Example differential equation and its significant contribution to the cooling of temperatures, which is one particular area of interest as far as the subject of real life situations, is concerned. Additionally, it is imperative to note that the first order differential equation that will be applied in determining the rate, timing and quantity of temperature cooling is an ordinary differential equation of first order. A first order differential equation conforms to the linearity of ordinary differential equations since the derivative part of the equation exists in the first degree (Abell & Braselton, 2004). As a result, the general representation of a first order differential equation of linear type can be represented by the following formula, Where dy/dx is the derivative part, P and Q are referred to as continuous functions of the variable x. in addition, X and y represents variables that are subject to manipulation. The above-mentioned formulation is the standard form of a first order linear differential equation, thus, the derivative solutions of such equation, first takes into consideration the re-writing of any equation in standard format before working on it in terms of derivation (Abell & Braselton, 2004). Moreover, if a differential equation contains coefficients preceding the derivative part, it is recommended that the coefficients be divided throughout the equation to ensure uniformity. When the derivative is preceded by a constant or any other variable they must be divided through the whole equation to obtain the standard form of the ordinary differential equation (Abell & Braselton, 2004). The analytical solution represents the general solution of the equations and it is imperative to note that it contains arbitrary constants, which can only be calculated, if there is the presence of initial value problems (Abell & Braselton, 2004). Therefore, the solution can be given by the following set of equations The numerical solution of a first order differential