- #1

m·x’’+(k+c·x’)·x^n=0

with m,c,k>0 and for exponent n --> 1<n<2

Any functional form for this equation??? I have solved it numerically but I would love if any functional analytical form exist...

Thanks!!

- A
- Thread starter Josu Aguirrebeitia
- Start date

- #1

m·x’’+(k+c·x’)·x^n=0

with m,c,k>0 and for exponent n --> 1<n<2

Any functional form for this equation??? I have solved it numerically but I would love if any functional analytical form exist...

Thanks!!

- #2

RPinPA

Science Advisor

Homework Helper

- 571

- 319

https://www.wolframalpha.com/input/?i=m·x(t)’’+(k+c·x(t)’)·x(t)^n=0

Solution: $$\alpha_1 + t = \int_1^{x(t)} \frac {c} {k\left(

-W\left(\frac

{-\sqrt[n+1]{\exp\left(\frac{c^2 \xi^{n+1}}{km}\right) - n - \frac{c^2n\alpha_1}{k} - \frac{c^2\alpha_1}{k} - 1}}

{k}\right)

\right) - k} d\xi$$

But then it also said the computation time was exceeded, so maybe there was more it could do with this.

If you have access to Mathematica, this is the code it generated to evaluate the expression.

Code:

`DSolve[{x[t]^n (k + c x'[t]) + m x''[t] == 0}, x[t], t]`

- #3

Thank you again!

J

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