Solving a Linear Differential Equation with a Square Root Term

[MrMumbleX]

Homework Statement

dv/dt = -327/3500 – (41/105)(square root of 6)(v²). Solve for v.

Homework Equations

The Attempt at a Solution

dv/[327/3500 + (41/105)(square root of 6)(v²)] = -dt
Then integrate both sides. 1/(square root of (327/3500)) * arctan(v * square root of ((41/105)(square root of 6)/(327/3500))) + c = -t?

 

[vela]

Almost right. You seem to be missing a factor of sqrt(105/41) on the lefthand side.

You can always check your answer by differentiating and seeing if you recover what you started with.