Question

what is the general solution for the following differential eqation? (x^4)-((c^4)x)=0,where c is a constant.

Answer 1

IT'S ANSWER IS X=0 OR X=C^(3/4)

Answer 2

how does that define a diffy q?

Answer 3

\[\frac{d^4x}{dt^4}-c^{4}x=0\]might be a better construction

Answer 4

in which case we would find the roots to the characteristic equation:
\[r^4-c^4=0\]
\[(r^2-c^2)(r^2+c^2)\]
\[(r-c)(r+c) (r^2+c^2)\]
\[(r-c)(r+c) (r=0\pm ci)\]
therefore:
\[x=a_1\ e^{-cx}+a_2\ e^{cx}+a_3\ cos(cx)+a_4\ sin(cx)\]