Differential equation problem

In summary, a differential equation is a mathematical equation that relates a function to its derivatives and is used to model and predict real-world phenomena. There are various types of differential equations, including first-order, second-order, and higher-order equations, and they can be solved using methods such as separation of variables, substitution, integration, and series solutions. Differential equations have many applications in fields such as physics, engineering, economics, biology, and chemistry.
  • #1
the7joker7
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Homework Statement



Find the value of k for which the constant function x(t)=k is a solution of the differential equation 9t[tex]_{2}[/tex][tex]\frac{dx}{dt}[/tex] -3x + 7 = 0.

The answer: k -2.33

Homework Equations



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The Attempt at a Solution



I'm a little confused on where to start...I was under the impression I had to factor and find what values would set the function equal to zero, so I did that, but it didn't come out right. Help?
 
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  • #2
Since x(t)=k doesn't have a term including t, we have dx/dt=0.The rest is just simple arithmetic!
 

What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves an independent variable, a dependent variable, and the derivative(s) of the dependent variable with respect to the independent variable.

What is the purpose of solving a differential equation?

The purpose of solving a differential equation is to find the general or particular solution(s) to the equation, which can then be used to model and predict the behavior of a system or phenomenon in the real world.

What are the different types of differential equations?

There are several types of differential equations, including first-order, second-order, and higher-order equations, as well as linear and nonlinear equations. Additionally, differential equations can be classified as ordinary or partial, depending on the type of derivatives involved.

What are the methods for solving differential equations?

There are various methods for solving differential equations, including separation of variables, substitution, integration, and series solutions. Other techniques such as Laplace transforms and numerical methods can also be used in certain cases.

What are some real-world applications of differential equations?

Differential equations have numerous applications in fields such as physics, engineering, economics, biology, and chemistry. They are used to model and analyze systems and phenomena such as population growth, fluid dynamics, electrical circuits, and chemical reactions.

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