Question

I can't seem to figure out this question.. Find the value of k for which the constant function x(t)=k is a solution of the differential equation 2t^4 dx/dt+8x+8=0. Now I thought I would solve for x(t)=... in terms of t and then say K=... However, the question says "Variable 't' is not defined in this context" so I am kind of lost. FYI I got x(t)=e^(4t^(-3)/3)-1 by variable separable

Answer 1

if \(x(t)=k\) is a solution to:\[\frac{dx}{dt}+8x+8=0\]then we know:\[\frac{dx}{dt}=0\quad\text{(since differential of a constant is zero)}\]therefore:\[0+8k+8=0\]and you should be able to solve this to find k.

Answer 2

It isn't dx/dt + 8x + 8, but 2t^4*dx/dt + 8x + 8

Answer 3

oh I see... It will give the same thing.. Facepalm :) Thanks ^^

Answer 4

yup :-)

Answer 5

yw