Need help solving second order DE.

[Joans]

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??

$$\frac{5\sqrt{3}}{18}\frac{d^{2}x}{dt^{2}} = 5 - \frac{3\sqrt{3}}{R}\frac{dx}{dt}$$

R is unknown.

$$\frac{d^{2}x}{dt^{2}} = x(t)$$

$$\frac{dx}{dt} = v(t)$$

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. :)

 

[rock.freak667]

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"

 

[Joans]

Yes R is a constant.
Okay I guess I understood a bit:

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

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 ?

 

[rock.freak667]

Since you have three unknowns you'd need at least one more condition to find R.

 

[Joans]

I understood, thanks for help!