First Order Differential Equation Help

Thread starter Bill Nye Tho
Start date Mar 7, 2013
Tags

Differential Differential equation First order First order differential

In summary, a first order differential equation is an equation that involves a function and its first derivative, used to represent the rate of change of a quantity over time. They are important because they are used to model real-world phenomena and make predictions about their behavior. There are different methods for solving these equations and they can have multiple solutions. First order differential equations are widely used in various fields of science to understand and predict the behavior of complex systems.

Mar 7, 2013

Bill Nye Tho

Homework Statement

dy/dx = 3 - 6x + y - 2xy

Homework Equations

dy/dx + p(x)y = c

p(y) dy = q(x) dx

The Attempt at a Solution

Just realized where my mistake was, sorry!

Last edited: Mar 7, 2013

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Mar 7, 2013

MostlyHarmless

You should leave your OP as it was and post your solution. In case someone else should have to same problem.

Related to First Order Differential Equation Help

1. What is a first order differential equation?

A first order differential equation is an equation that involves a function and its first derivative. It represents the rate of change of a quantity over time.

2. Why do we need to solve first order differential equations?

First order differential equations are used to model many real-world phenomena, such as population growth, chemical reactions, and physical systems. Solving these equations allows scientists to make predictions and understand the behavior of these systems.

3. How do I solve a first order differential equation?

There are several methods for solving first order differential equations, including separation of variables, integrating factors, and using power series. The specific method used will depend on the form of the equation and the initial conditions given.

4. Can first order differential equations have multiple solutions?

Yes, some first order differential equations can have multiple solutions. This is known as the existence and uniqueness theorem, which states that a first order differential equation with continuous coefficients and initial conditions will have a unique solution if a certain condition is met.

5. How are first order differential equations used in science?

First order differential equations are used in various fields of science, including physics, biology, chemistry, economics, and engineering. They help to model and understand complex systems and make predictions about their behavior.