NDSolve

NDSolve[eqns,u,{x,xmin,xmax}] finds a numerical solution to the ordinary differential equations eqns for the function u with the independent variable x in the range xmin to xmax. 

NDSolve[eqns,u,{x,xmin,xmax},{y,ymin,ymax}] solves the partial differential equations eqns over a rectangular region.

NDSolve[eqns,u,{x,y}∈Ω] solves the partial differential equations eqns over the region Ω.

NDSolve[eqns,u,{t,tmin,tmax},{x,y}∈Ω] solves the time-dependent partial differential equations eqns over the region Ω.

NDSolve[eqns,{u1,u2,…},…] solves for the functions ui. 

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