Explain differential equation of order 3?

In summary, a differential equation of order 3 is a higher order differential equation that involves the third derivative of a function and requires three initial conditions to be fully determined. It is used to model physical phenomena and solve complex problems in engineering and physics. To solve it, techniques such as separation of variables and integration by parts are used, along with the initial conditions. The benefits of using a differential equation of order 3 include its ability to provide a mathematical framework for understanding and predicting natural processes, making it a valuable tool in various fields of science and engineering.
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Explain differential equation of order 3? With example?
 
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A differential equation of order three is an equation with an unknown function that involves the third derivative of that function.

Examples:

[tex]\frac{d^3y}{dx^3}= 0[/itex]
where y is an unknown function of x.

[tex]y^2\frac{d^3y}{dt^3}- 7y\frac{d^2y}{dt^2}+ sin(y)\frac{dy}{dt}+ e^{ty}= ln(t)[/tex]
where y is an unknown function of t.
 

FAQ: Explain differential equation of order 3?

What is a differential equation of order 3?

A differential equation of order 3 is a type of differential equation that involves a function and its derivatives up to the third order. It can be represented as f'''(x) + g''(x) + h'(x) + i(x) = 0.

How is a differential equation of order 3 different from other types of differential equations?

A differential equation of order 3 is different from other types of differential equations because it involves the third derivative of the function, making it a higher order equation. This means that the solution will involve three constants and will require three initial conditions to be fully determined.

What are some real-world applications of differential equations of order 3?

Differential equations of order 3 can be used to model various physical phenomena such as the motion of a pendulum, the vibrations of a guitar string, and the behavior of electrical circuits. They are also commonly used in engineering and physics to solve complex problems.

How do you solve a differential equation of order 3?

In order to solve a differential equation of order 3, you will need to use techniques such as separation of variables, substitution, or integration by parts. You will also need to use the initial conditions to find the values of the three constants in the solution.

What are the benefits of using a differential equation of order 3?

Differential equations of order 3 allow us to model and understand complex processes and phenomena in the natural world. They provide a mathematical framework for solving problems and making predictions, making them an important tool in various fields of science and engineering.

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