Need help solving second order DE.

In summary, the conversation is about a student who is struggling to solve a differential equation for their problem. They are unsure if it is even possible to solve and are seeking help. Another person suggests a method for solving the equation and the student expresses their understanding and thanks for the help.
  • #1
Joans
22
0
Hello, I hope I am writing to right part of a forum...

I made a differential equation when I was solving my problem, but unfortunately I am not capable of solving such equation since I am only 12th grader.
Or maybe it is not possible to solve it at all??

[tex] \frac{5\sqrt{3}}{18}\frac{d^{2}x}{dt^{2}} = 5 - \frac{3\sqrt{3}}{R}\frac{dx}{dt}[/tex]

R is unknown.

[tex]\frac{d^{2}x}{dt^{2}} = x(t) [/tex]

[tex]\frac{dx}{dt} = v(t)[/tex]

v(0) = 0
v(5) = 15

I need to find equation describing x(t). Jap, v is velocity, and nope it is not my homework.

It would be great if someone help me a bit, in school do not teach how to solve differential equations, nor second order. :)
 
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  • #2
If R is constant, then you have a 2nd order DE with constant coefficients. Which can be solved by writing down the roots of the auxiliary equation.
http://www.efunda.com/math/ode/linearode_consthomo.cfm"
 
Last edited by a moderator:
  • #3
Yes R is a constant.
Okay I guess I understood a bit:

[tex]x(t) = c_{1}e^{\frac{18(\sqrt{\frac{27}{R^{2}}+\frac{50\sqrt{3}}{9}}-\frac{3\sqrt{3}}{R})}{5\sqrt{3}}t}+c_{2}e^{-\frac{18(\sqrt{\frac{27}{R^{2}}+\frac{50\sqrt{3}}{9}}+\frac{3\sqrt{3}}{R})}{5\sqrt{3}}t}[/tex]

anyway to me it gets too crazy.

x(0)'=0
x(5)'=15

is it possible to solve this equation normally that I would know R & c1 & c2 ?
 
Last edited:
  • #4
Since you have three unknowns you'd need at least one more condition to find R.
 
  • #5
I understood, thanks for help!
 

What is a second order differential equation?

A second order differential equation is a mathematical equation that involves the second derivative of an unknown function. It is commonly used to model physical systems in science and engineering.

How do I solve a second order differential equation?

To solve a second order differential equation, you need to first identify the type of equation it is (homogenous, non-homogenous, linear, etc.). Then, you can use various methods such as separation of variables, variation of parameters, or Laplace transforms to find the solution.

What are the applications of second order differential equations?

Second order differential equations are used in various fields, including physics, engineering, economics, and biology, to model a wide range of systems such as oscillations, circuits, population growth, and chemical reactions.

Do I need to know calculus to solve second order differential equations?

Yes, a strong understanding of calculus is necessary to solve second order differential equations. You will need to know how to take derivatives and integrals, as well as other techniques such as substitution and integration by parts.

Are there any online resources available for help with solving second order differential equations?

Yes, there are many online resources available, including video tutorials, practice problems, and step-by-step guides for solving different types of second order differential equations. You can also seek help from online forums or hire a tutor for personalized assistance.

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