# Is the differential equation solvable?

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.

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.