# Differential Equations MATLAB Homework Help

A differential equation is a mathematical equation that relates an unknown function of one or more variables that with its derivatives. The differential equations arise whenever a deterministic relation involving some continuously varying quantities (modeled by functions) and their rates of change in space and/or time (expressed as derivatives) is known or postulated. Due to such relations are extremely common, the differential equations play a prominent role in many disciplines including engineering, the physics, the economics, the biology.

Differential equations are mathematically studied from several different perspectives, which mostly concerned with their solutions the set of functions that satisfy the equation. The simplest differential equations admit solutions given by explicit formulas; some properties of solutions of a given differential equation may be determined without finding their exact form. In case if a self-contained formula for the solution is not available, solution may be numerically approximated using computers. Theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, where many numerical methods have been developed to determine solutions with a given degree of accuracy.

Function to solve the differential equation:

Dsolve

## Syntax

S = dsolve(eqn)
S = dsolve(eqn,cond)
S = dsolve(eqn,cond,Name,Value)
Y = dsolve(eqns)
Y = dsolve(eqns,conds)
Y = dsolve(eqns,conds,Name,Value)
[y1,...,yN] = dsolve(eqns)
[y1,...,yN] = dsolve(eqns,conds)
[y1,...,yN] = dsolve(eqns,conds,Name,Value)

## Description

S = dsolve(eqn) solves the ordinary differential equation eqn. eqn is a symbolic equation containing diff to indicate derivatives. You can use a string with the letter D indicating derivatives. For example, syms y(x); dsolve(diff(y) == y + 1) and dsolve('Dy = y + 1','x') both solve the equation dy/dx = y + 1 with respect to the variable x. eqn can be an array of such equations or strings.

S = dsolve(eqn,cond) solves the ordinary differential equation eqn with the initial or boundary condition cond.

S = dsolve(eqn,cond,Name,Value) uses additional options specified by one or more Name,Value pair arguments.

Y = dsolve(eqns) solves the system of ordinary differential equations eqns and returns a structure array that contains the solutions. Number of fields in the structure array corresponds to the number of independent variables in the system.

Y = dsolve(eqns,conds) solves the system of ordinary differential equations eqns with the initial or boundary conditions conds.

Y = dsolve(eqns,conds,Name,Value) which uses additional options specified by one or more Name,Value pair arguments.

[y1,...,yN] = dsolve(eqns) solves the system of ordinary differential equations eqns and assigns the solutions to the variables y1,...,yN.

[y1,...,yN] = dsolve(eqns,conds) solves the system of ordinary differential equations eqns with the initial or boundary conditions conds.

[y1,...,yN] = dsolve(eqns,conds,Name,Value) uses additional options specified by one or more Name,Value pair arguments.

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