Solution of differential equation

Thread starter 2rashmi1993
Start date Oct 21, 2010
Tags

Differential Differential equation

In summary, a differential equation is a mathematical equation that relates functions and their derivatives to describe the change of a quantity over time or in relation to other variables. Solving a differential equation allows us to find the function(s) that represent the behavior of a system, and there are various methods for solving them including separation of variables, substitution, integration, and using special functions. To verify a solution, one can substitute the proposed solution into the original equation or plot it to match the expected behavior. Differential equations have many applications in science, including physics, chemistry, biology, engineering, and economics, to model and understand complex systems.

Oct 21, 2010

2rashmi1993

How do we/ can we find the solution of a differential eq d^3y/dx^3 + d^2y/dx^2 - dy/dx =0?

Physics news on Phys.org

Oct 21, 2010

JJacquelin

Let z=dy/dx and rewrite the EDO as a classical second order linear EDO.

Oct 21, 2010

g_edgar

Or: think of it as a linear DE with constant coefficients, and consult the method for that in your textbook.

1. What is a differential equation?

A differential equation is a mathematical equation that relates one or more functions and their derivatives. It describes how a quantity changes over time or in relation to other variables.

2. What is the purpose of solving a differential equation?

The purpose of solving a differential equation is to find the function(s) that satisfy the equation and represent the behavior of a system. This allows us to make predictions and understand the underlying principles governing the system.

3. What are the different methods for solving a differential equation?

The most common methods for solving differential equations are separation of variables, substitution, integration, and using special functions such as Laplace transforms or power series.

4. How do you verify the solution of a differential equation?

To verify the solution of a differential equation, you can substitute the proposed solution into the original equation and see if it satisfies the equation. Another method is to plot the solution and see if it matches the expected behavior of the system.

5. What are the applications of differential equations in science?

Differential equations are used in many fields of science, including physics, chemistry, biology, engineering, and economics. They are used to model and understand complex systems, such as the motion of objects, population growth, chemical reactions, and electrical circuits.