First order differential equations

In summary, the speaker is seeking guidance on how to approach differential equations and specifically how to determine if an equation is homogeneous or exact. They note that solving exact equations is typically easier, and ask if an equation can be considered as both homogeneous and exact. They also express gratitude for a previous helpful response.
  • #1
missmee
2
0
good day everyone.
i need to know what test must i make first in dealing with differential equations.. please help me. it's hard for me to figure out whether an equation is homogeneous or exact... there are examples of exact differential equations that have same degrees for M(x,y) and N(x,y)..if that's the case, should i consider it as homogeneous before considering it as exact?
 
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  • #2
Typically, it is easier to solve an "exact" equation than it is to solve a "homogeneous" equation so if I had an equation that was both, I would first try solving it as I would an exact equation.
 
  • #3
HallsofIvy, thank you for your reply,. it helped me. :) Thank you. :)
 

FAQ: First order differential equations

What is a first order differential equation?

A first order differential equation is an equation that involves the derivative of a function with respect to one independent variable. It can be written in the form dy/dx = f(x,y), where y is the dependent variable and x is the independent variable.

What is the order of a differential equation?

The order of a differential equation is the highest derivative that appears in the equation. A first order differential equation contains only the first derivative, while a second order differential equation contains the second derivative and so on.

What is the general solution of a first order differential equation?

The general solution of a first order differential equation is a solution that contains all possible solutions to the equation. It usually includes a constant of integration, which can take different values for different specific solutions.

What is an initial value problem for a first order differential equation?

An initial value problem for a first order differential equation is a specific type of problem where a unique solution is found by specifying the value of the dependent variable at a certain value of the independent variable. This value is called the initial condition, and it allows us to find the particular solution that passes through that point.

What are some applications of first order differential equations?

First order differential equations have many applications in various fields such as physics, chemistry, biology, economics, and engineering. They can be used to model rates of change, growth and decay, and many other real-world phenomena. Examples include Newton's law of cooling, population growth, and radioactive decay.

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