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Solving 2nd order PDE into Mathematica


Hello,

I saw that DSolve can not solve a 2nd order pde like this

pde=-D[f[x,t],x]+D[f[x,t],{x,2}]==D[f[x,t],t]

but I would like to know if someone has already implemented some other 
procedure to solve it 

Thank you in advance
Paolo


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