Name of a type of differential equations

In summary, ordinary differential equations (ODEs) are equations that involve one or more independent variables, a dependent variable, and its derivatives. They are used to model relationships or describe the behavior of systems over time. On the other hand, partial differential equations (PDEs) involve two or more independent variables and their partial derivatives, and are used to model relationships that vary in space and time. These types of equations are used in various fields of science, such as physics, engineering, biology, and economics, to predict and understand complex systems. The order of a differential equation is determined by the highest derivative present in the equation, and linear and nonlinear differential equations differ in their relationship between the dependent variable and its derivatives. Linear equations are easier
  • #1
kevchang
3
0
Dear all,

I am interested in solving the following type of system of differential equations for η(x):

(1) ∫η(x)ω(x)=0
(2) ∫η'(x)ω(x)=0

for known ω(x), and known limits of the integral. Does this type of equations have a name? Can someone help me to find some reference? Thanks a ton!

Cheers,
Kev
 
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  • #2
These are Fredholm integral equations of the first kind.
 

What are ordinary differential equations?

Ordinary differential equations (ODEs) are mathematical equations that involve one or more independent variables, a dependent variable, and its derivatives. They are used to model relationships between physical quantities or describe the behavior of a system over time.

What are partial differential equations?

Partial differential equations (PDEs) are mathematical equations that involve two or more independent variables and their partial derivatives. They are used to model relationships between physical quantities that vary in space and time.

How are differential equations used in science?

Differential equations are used in many scientific fields, including physics, engineering, biology, and economics. They are used to model and predict the behavior of complex systems, such as the motion of objects, the growth of populations, or the flow of fluids.

What is the order of a differential equation?

The order of a differential equation is the highest derivative present in the equation. For example, a first-order differential equation has only first derivatives, while a second-order differential equation has second derivatives.

What is the difference between linear and nonlinear differential equations?

Linear differential equations have a linear relationship between the dependent variable and its derivatives, while nonlinear differential equations have a nonlinear relationship. Linear differential equations are easier to solve analytically, while nonlinear differential equations often require numerical methods.

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