Find 'k' for x(t)=k is solution for diff eq

[mesa]

Homework Statement

Find the value of k for which the constant function x(t)=k is a solution of the differential equation 6t^5dx/dt+7x−4=0.

The Attempt at a Solution

I have tried this several ways but no luck, here is one of my attempts,

solve for dx/dt,

dx/dt = (4-7x)/6t^5

take the integral,

x(t) = (1/6t^5)(4x-7x^2/2)

and that doesn't help :P
I am sure as usual I am missing something straightforward but I don't see it.

 

[STEMucator]

You have $x(t) = k$ therefore $x'(t) = 0$.

Plugging those in yields :

$(6t^5)(0) + 7k − 4= 0$

I'm sure that you got this now. It's the same concept as in your prior thread.

 

[mesa]

You have $x(t) = k$ therefore $x'(t) = 0$.

Plugging those in yields :

$(6t^5)(0) + 7k − 4= 0$

I'm sure that you got this now. It's the same concept as in your prior thread.

You know...
At least missing these types of things typically only happens once.

Thanks again!