Solving Higher Order Differential Equation

In summary, the conversation discusses the purpose and physical meaning of higher order derivatives in mathematics. The first and second derivatives are known as the rate and acceleration respectively, but the third and higher derivatives do not have a specific interpretation in mechanics. However, they can be useful in calculating various mathematical quantities. The conversation also includes a humorous comment about not needing higher order derivatives in carpentry.
  • #1
rsvsk4live
1
0
Hi Friends,

Could anyone answer my question please I am not good in math:

Why we do Higher order derivatives..? What its physical meaning ...?

we keep on finding the derivatives till we get function zero...why...?

Lets say my equation is Y= x3 + 3x2 + 3x + 2

Thanks

Rsvsk
 
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  • #2
Welcome to PF!

rsvsk4live said:
Why we do Higher order derivatives..? What its physical meaning ...?

we keep on finding the derivatives till we get function zero...why...?

Lets say my equation is Y= x3 + 3x2 + 3x + 2

Hi Rsvsk! Welcome to PF! :smile:

As you know, the first derivative is the rate (or speed), and the second derivative is the acceleration, so I assume you're wondering what the third derivative is?

Well, it isn't anything in particular …

in mechanics, for example, you wouldn't usually need third or higher derivatives.

But they can be useful in calculating volumes, expansions, approximations, and other things. :smile:
 
  • #3


tiny-tim said:
Well, it isn't anything in particular …

in mechanics, for example, you wouldn't usually need third or higher derivatives.
Ha ha ha.
I guess you also do not need third or higher order tensors, differential equations, triple integrals or the calculus of variation. In carpentry you don't need nails.
Yoy can call x,x',x'',x''',x'''',x''''',x''''''
Position, Velocity, Acceleration ,Jerk/Jolt, Snap, Crackle, Pop

edited to say:At least you said usually, although I do not know what you meant by it.
 
  • #4
lurflurf said:
At least you said usually, although I do not know what you meant by it.

my lawyer told me to put that in! :wink:
 

What is a higher order differential equation?

A higher order differential equation is a mathematical equation that involves derivatives of a function up to a certain order. For example, a second order differential equation involves the second derivative of a function, while a third order differential equation involves the third derivative. Higher order differential equations are commonly used to model physical systems in various fields of science and engineering.

What is the process for solving a higher order differential equation?

The process for solving a higher order differential equation involves finding a general solution that satisfies the equation for all possible values of the independent variable. This is typically done by using techniques such as separation of variables, variation of parameters, or by finding the eigenvalues and eigenvectors of the equation.

What are the applications of solving higher order differential equations?

Solving higher order differential equations is crucial in many scientific fields, including physics, engineering, economics, and biology. It can be used to model the behavior of physical systems, predict the motion of objects, analyze economic trends, and understand biological processes.

What are the initial conditions in a higher order differential equation?

The initial conditions in a higher order differential equation are the values of the dependent variable and its derivatives at a specific point in the independent variable. These conditions are necessary to determine a unique solution to the equation.

Can all higher order differential equations be solved analytically?

No, not all higher order differential equations can be solved analytically. Some equations may have complex or non-elementary functions as solutions, while others may not have closed-form solutions at all. In these cases, numerical methods can be used to approximate the solutions.

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