Question: Partial differential operators

I want to construct equation  equation LT−TL=0, where L and T represent partial differential operators as

L = u^2 * ∂^2/∂x^2 + ∂/∂y

T = 4u^3 * ∂^3/∂x^3 + (6u^2u_x - 6u^2 * ∂^(-1)/∂x(u_y/u^2)) * ∂/∂x - ∂/∂t.

Could you please provide Maple code to accomplish this task??

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