Is the differential equation solvable?

[davedave]

Here is the question. Find the steady state solution of the differential equation below.

dy/dx = tan(x^2)

What makes this one difficult is that the tangent has no elementary function.

Can anyone explain how to find the steady state solution? Thanks.

 

[HallsofIvy]

The problem does not ask you to solve the equation. An "equilibrium" solution, or "steady state" solution for a problem like this is a constant function. That means that dx/dt= 0. So you only have to solve $tan(x^2)= 0$. Of course, because tangent is a periodic function, there will be many solutions to that.