Question

Find the value of k for which the constant function x(t)=k is a solution of the differential equation \displaystyle 7 t^4 \frac{dx}{dt} - 8 x - 3 = 0

Answer 1

\[x=k~~\implies~~\frac{dx}{dt}=0\]
Substitute into the equation:
\[\frac{dx}{dt}-8x-3=0~~\iff~~0-8k-3=0\]
Solve for \(k\).

Answer 2

thank you, I was able to solve and got the right answer but how does 7t^4(dx/dt) become only dx/dt?

Answer 3

\(\dfrac{dx}{dt}=0\), and so \(7t^4\cdot0=0\).

Answer 4

Sorry, I actually didn't notice the \(7t^4\) until now... It doesn't affect what the answer is though.

Answer 5

Thank you for your help!!