Write a differential equation that fits the physical description. The velocityvelocity of a particle movingof a particle moving along a straight linealong a straight line at time t is proportional to the fourthfourth power of its position xposition x.

The differential equation is

dx/dt - Kx^4 = 0

Step-by-step explanation:

Let V represent the velocity of the particle moving along a straight line at time t.

We have the position to be x.

Then we have that

V is proportional to x^4

=> V = Kx^4

Where K is constant of proportionality.

Velocity is the derivative of the position vector with respect to time t, so we can write

V = dx/dt

And then

dx/dt = Kx^4

So that

dx/dt - Kx^4 = 0

This is the differential equation