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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(л, t) 3 (ах + ы)e
satisfies the Dym equation for all (x, t) with ax + bt > 0.

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