# How To Solve An Initial Value Problem

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A differential equation is called an ordinary differential equation, abbreviated by ode, if it has ordinary derivatives in it.$\beginay'' by' cy = g\left( t \right)\label\end$ $\begin\sin \left( y \right)\frac = \left( \right)\frac \label\end$ $\begin 10y''' - 4y' 2y = \cos \left( t \right) \label\end$ $\begin\frac = \frac\label\end$ $\begin = \label\end$ $\begin\frac = 1 \frac \label\end$ The order of a differential equation is the largest derivative present in the differential equation.In the differential equations listed above $$\eqref$$ is a first order differential equation, $$\eqref$$, $$\eqref$$, $$\eqref$$, $$\eqref$$, and $$\eqref$$ are second order differential equations, $$\eqref$$ is a third order differential equation and $$\eqref$$ is a fourth order differential equation.$\begina = \frac\hspace\hspace\,\,\,\,\,\,a = \frac \label\end$ Where $$v$$ is the velocity of the object and $$u$$ is the position function of the object at any time $$t$$.We should also remember at this point that the force, $$F$$ may also be a function of time, velocity, and/or position.Only the function,$$y\left( t \right)$$, and its derivatives are used in determining if a differential equation is linear.If a differential equation cannot be written in the form, $$\eqref$$ then it is called a non-linear differential equation.Also note that neither the function or its derivatives are “inside” another function, for example, $$\sqrt$$ or .The coefficients $$\left( t \right),\,\, \ldots \,\,,\left( t \right)$$ and $$g\left( t \right)$$ can be zero or non-zero functions, constant or non-constant functions, linear or non-linear functions.A linear differential equation is any differential equation that can be written in the following form.$\begin \left( t \right)\left( t \right) \left( t \right)\left( t \right) \cdots \left( t \right)y'\left( t \right) \left( t \right)y\left( t \right) = g\left( t \right) \label\end$ The important thing to note about linear differential equations is that there are no products of the function, $$y\left( t \right)$$, and its derivatives and neither the function or its derivatives occur to any power other than the first power.

## Comments How To Solve An Initial Value Problem

• ###### IVP's with Mathematica's Solver

Solving Initial Value Problems with Mathematica's Solver. Hopefully you recall asking Mathematica to give the syntax of its DSolve command in an earlier.…

• ###### Using Matlab for solving ODEs initial value problems

This type of problem is known as an Initial Value Problem IVP. In order to solve these we use the inbuilt MATLAB commands ode45 and ode15s, both of which.…

• ###### Example Solving a First-Order ODE Initial Value Problem

The output, fyk, is a function of a function, so you must specify the value of the parameter for which you would like the solution function. 4. Assign the result to an.…

• ###### Solution of initial value problems for first order systems using.

Of Clifford Analysis turns out to be elliptic, parabolic or hyperbolic See Mrs. E. Obolashvili's paper 13 and the book 14 of the same author where one can find.…

• ###### Initial Value Problem - Teaching Concepts with Maple.

The initial value problem for a driven damped oscillator is solved with the ODE Analyzer Assistant, which provides the analytic solution and its graph. A stepwise.…

• ###### Solving an initial value problem with ode45 - UMD MATH

You need to download an m-file. You have to download the m-file dirfield.m. format short g. Initial value problem. We consider the initial value problem. y'=y-t.…

• ###### Initial value problems - Scholarpedia

Feb 25, 2007. that are to hold on a finite interval t_0, t_f\. An initial value problem specifies the solution of interest by an initial condition yt_0 = A\.…