What Value of k Makes x(t)=k a Solution to the Differential Equation?

[the7joker7]

Homework Statement

Find the value of k for which the constant function x(t)=k is a solution of the differential equation 9t_{2}\frac{dx}{dt} -3x + 7 = 0.

The answer: k -2.33

Homework Equations

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The Attempt at a Solution

I'm a little confused on where to start...I was under the impression I had to factor and find what values would set the function equal to zero, so I did that, but it didn't come out right. Help?

 

[sylar]

Since x(t)=k doesn't have a term including t, we have dx/dt=0.The rest is just simple arithmetic!