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# What is an initial condition in differential equations?

## What is an initial condition in differential equations?

An initial condition is an extra bit of information about a differential equation that tells you the value of the function at a particular point. Differential equations with initial conditions are commonly called initial value problems.

## What are initial conditions in PDE?

PDE’s are usually specified through a set of boundary or initial conditions. A boundary condition expresses the behavior of a function on the boundary (border) of its area of definition. An initial condition is like a boundary condition, but then for the time-direction.

Do initial conditions matter?

The number of required initial pieces of information is the dimension n of the system times the order k = 1 of the system, or n. The initial conditions do not affect the qualitative behavior (stable or unstable) of the system.

### What is an example of initial condition?

Initial Condition(s) Example 2 y(x)=x−32 y ( x ) = x − 3 2 is a solution to 4x2y′′+12xy′+3y=0 4 x 2 y ″ + 12 x y ′ + 3 y = 0 , y(4)=18 y ( 4 ) = 1 8 , and y′(4)=−364 y ′ ( 4 ) = − 3 64 .

### How do you plot a differential equation in maple?

You can use the ‘type=numeric’ option with the ‘dsolve’ routine to generate a numerical approximation to the solution of a system of ordinary differential equations.

What does Dsolve do in Maple?

For a given system of equations and set of initial conditions, dsolve will attempt to find an explicit solution. If no suitable explicit solution can be found, then dsolve will display a warning and return an implicit solution.

#### What is meant by initial conditions?

Definition of initial condition : any of a set of starting-point values belonging to or imposed upon the variables in an equation that has one or more arbitrary constants.

#### What is initial condition math?

In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0).

Why are initial conditions needed?

For a system of order k (the number of time lags in discrete time, or the order of the largest derivative in continuous time) and dimension n (that is, with n different evolving variables, which together can be denoted by an n-dimensional coordinate vector), generally nk initial conditions are needed in order to trace …