# Write an equivalent first-order differential equation and initial condition for y

By our assumption can be approximated by the derivative of the constructed interpolating polynomial: Here interpolating parabola are defined by the system we assume for simplicity: After subtracting first equation from the last we get final result: In the same way we can obtain expressions for any. The reason why the father wished to close down the branch was that it appeared to be making a loss. However, it is quite the reverse; if the branch was closed then, the positive contribution from the branch would be lost and overall profits would fall.

This is because the indirect costs of production do not vary with output and, therefore, closure of a section of the firm would not lead to immediate savings.

This may mean that closing the branch would be a mistake on financial grounds.

The whole point of this is to notice that systems of differential equations can arise quite easily from naturally occurring situations. Developing an effective predator-prey system of differential equations is not the subject of this chapter. However, systems can arise from $$n^{\text{th}}$$ order linear differential equations as well. Nov 04,  · A partial differential equation (or briefly a PDE) is a mathematical equation that involves two or more independent variables, an unknown function (dependent on those variables), and partial derivatives of the unknown function with respect to the independent benjaminpohle.com order of a partial differential equation is the order of the highest derivative involved. 2) Consider the system of differential equations. dx/dt=−5y dy/dt=−5x. convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for x from the first equation%(1).

This mistake is made due to a misunderstanding of nature of cost behavior. If the branch is closed then the only costs that would be saved are the costs directly related to the running of the branch: The costs are indirect in nature, in this example the marketing and central administration costs, would still have to be paid as they are unaffected by output.

For this decision to be made, we should use contribution as a guide for deciding whether or not to close a branch. This can also be applied to the production of certain product lines, or the cost effectiveness of departments. On financial grounds, contribution is therefore, a better guide in making decisions.Box and Cox () developed the transformation.

Estimation of any Box-Cox parameters is by maximum likelihood. Box and Cox () offered an example in which the data had the form of survival times but the underlying biological structure was of hazard rates, and the transformation identified this.

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.. The term difference equation sometimes (and for the purposes of this article) refers to a specific type of recurrence relation. Here is a history of questions and answers processed by "Ask the Physicist!". If you like my answer, please consider making a donation to help support this service..

If there is a link to a previously answered question, be patient. Equivilent first order differential and initial condition? Writing equivalent first order differential equation and initial condition. 2. The initial condition for a heat equation with stationary solution subtracted. 1. Delay Differential Equation - derivation of initial condition.

0. The initial condition for first order differential equations will be of the form $y\left({{t_0}} \right) = {y_0}$ Recall as well that a differential equation along with a sufficient number of initial conditions is called an Initial Value Problem (IVP).

First Order Diﬀerential Equations FIRST ORDER LINEAR DIFFERENTIAL EQUATION The ﬁrst order diﬀeren-tial equation y0 = f(x,y)isalinear equation if it can be written in the form if an initial condition is speciﬁed, then the constant C will be uniquely determined.

Thus.

Differential Equations - Systems of Differential Equations