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I am wondering how to solve this heat equation with a 'generation' term included. In one instance I am adding the generation term, in the other I am subtracting it.

[tex] a\frac{\partial^{2}f }{\partial x^{2}}-\frac{\partial f}{\partial t} - \lambda f = 0[/tex]

[tex] a\frac{\partial^{2}f }{\partial x^{2}}-\frac{\partial f}{\partial t} + \lambda f = 0[/tex]

Any information on how to solve these/links to a table would be great :D