What is initial value problem in differential equation?

In multivariable calculus, an initial value problem (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem.

What is the use of DSolve command in Mathematica?

solves a differential equation for the function u, with independent variable x. solves a differential equation for x between xmin and xmax. solves a list of differential equations.

What do initial conditions mean?

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 Dsolve?

S = dsolve( eqn ) solves the differential equation eqn , where eqn is a symbolic equation. Use diff and == to represent differential equations. For example, diff(y,x) == y represents the equation dy/dx = y. Solve a system of differential equations by specifying eqn as a vector of those equations.

How do I specify initial conditions for an equation?

To specify initial conditions, enclose the equation and the initial conditions ( and ) in a list: Copy to clipboard. If not enough initial conditions are given, constants C [ n] are returned:

How do I solve differential equations in Wolfram Language?

The Wolfram Language’s differential equation solving functions can be applied to many different classes of differential equations, automatically selecting the appropriate algorithms without needing preprocessing by the user. Use DSolve to solve the differential equation for with independent variable :

How can I graph the solutions to an underspecified differential equation?

You can use DSolve, /., Table, and Plot together to graph the solutions to an underspecified differential equation for various values of the constant. First, solve the differential equation using DSolve and set the result to solution:

How to solve the differential equation for with independent variable?

Use DSolve to solve the differential equation for with independent variable : Copy to clipboard. The solution given by DSolve is a list of lists of rules. The outermost list encompasses all the solutions available, and each smaller list is a particular solution.

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