4. The Dym equation du is a nonlinear evolution equation which arises in the study of the motion of the interface between a viscous and a nonviscous fluid with surface tension. Find all nonzero constants a, b, c such that the function u(x, t) = (ax+ bt)e %3D satisfies the Dym equation for all (x, t) with ax + bt > 0.

4. The Dym equation du is a nonlinear evolution equation which arises in the study of the motion of the interface between a viscous and a nonviscous fluid with surface tension. Find all nonzero constants a, b, c such that the function u(x, t) = (ax+ bt)e %3D satisfies the Dym equation for all (x, t) with ax + bt > 0.