Solving Trivial Second Order ODEs

In summary: So, to summarize, to solve an ODE of the form y'' = 0, one can integrate twice and use the boundary conditions to find the constants. In this case, the integral of 0 is 0, plus an arbitrary constant (A), and the integral of A is Ax, plus another arbitrary constant (B). Hope that helps!
  • #1
terryphi
59
0
Hey,

I feel kind of stupid for asking this, but how does one solve an ODE of the form y'' = 0

I know it's Ax+B=0 but I forgot how I got there.

Cheers,
 
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  • #2
The integral of 0 is 0, plus an arbitrary constant (call it A).
The integral of A is Ax, plus another arbitrary constant (call it B).
 
  • #3
terryphi said:
Hey,

I feel kind of stupid for asking this, but how does one solve an ODE of the form y'' = 0

I know it's Ax+B=0 but I forgot how I got there.

Cheers,

I believe the answer is by integrating twice:

y'' = d2y/dx2 = 0
[tex]
\int y'' dx = \int 0 dx = A
[/tex]
(A is a const)

and again:

[tex]
\int A dx = Ax +B
[/tex]
(B is a const)

Get two constants as it is second order and find the constants using the boundary conditions...
Hope that helps
 
  • #4
Heh, thanks..forgot the integral of 0 was C

rfwebster said:
I believe the answer is by integrating twice:

y'' = d2y/dx2 = 0
[tex]
\int y'' dx = \int 0 dx = A
[/tex]
(A is a const)

and again:

[tex]
\int A dx = Ax +B
[/tex]
(B is a const)

Get two constants as it is second order and find the constants using the boundary conditions...
Hope that helps
 
  • #5
easy thing to forget!
 

FAQ: Solving Trivial Second Order ODEs

What is a Second Order ODE?

A Second Order ODE (Ordinary Differential Equation) is a type of mathematical equation that involves a function and its first and second derivatives. It can be solved to find the function that satisfies the equation.

How do I solve a Second Order ODE?

To solve a Second Order ODE, you can use various techniques such as separation of variables, substitution, or using a integrating factor. It is important to follow the correct steps and manipulate the equation to isolate the function.

Can all Second Order ODEs be solved analytically?

No, not all Second Order ODEs can be solved analytically. Some equations may have solutions that cannot be expressed in terms of elementary functions. In such cases, numerical methods or approximations can be used to find solutions.

What are the applications of solving Second Order ODEs?

Second Order ODEs have many applications in physics, engineering, and other fields of science. They can be used to model and understand various phenomena, such as motion, vibrations, and electrical circuits.

Are there any tips for solving Second Order ODEs more efficiently?

One tip for solving Second Order ODEs more efficiently is to practice and familiarize yourself with different techniques and methods. It is also important to carefully analyze the equation and choose the most suitable method for solving it. Additionally, breaking down the problem into smaller steps and checking your work can help avoid mistakes and make the process more efficient.

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