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

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Thank you for your help!!