EXAMPLE:  This is a plot to the solution to the heat equation on an infinite rod, with k=1 and the initial condition f(x)=1 for |x|<2 and zero elsewhere. 

 

 

> z1:=(x+2)/sqrt(2*sqrt(t)); z2:=(x-2)/sqrt(2*sqrt(t));
 

 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(x, 2), `*`(`^`(2, `/`(1, 2))))), `*`(`^`(t, `/`(1, 4)))))
`+`(`/`(`*`(`/`(1, 2), `*`(`+`(x, `-`(2)), `*`(`^`(2, `/`(1, 2))))), `*`(`^`(t, `/`(1, 4))))) (1)
 

> F:=(5/2)*(erf(z1)-erf(z2));
 

`+`(`*`(`/`(5, 2), `*`(erf(`+`(`/`(`*`(`/`(1, 2), `*`(`+`(x, 2), `*`(`^`(2, `/`(1, 2))))), `*`(`^`(t, `/`(1, 4)))))))), `-`(`*`(`/`(5, 2), `*`(erf(`+`(`/`(`*`(`/`(1, 2), `*`(`+`(x, `-`(2)), `*`(`^`(2,... (2)
 

> animate(plot,[F,x=-6..6],t=0..2);
 

Plot_2d
 

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