Question: Issues with pdsolve

PDE1 := diff(f(x, t), t) = diff(f(x, t), x, x)+a*f(x, t); pdsolve([PDE1, f(x, 0) = 1])

will give me

f(x, t) = exp(t*a)

which is indeed a solution of the PDE1

PDE2 := diff(g(t, x), t) = diff(g(t, x), x, x)+a*g(t, x); pdsolve([PDE2, g(0, x) = 1])

will give me

g(t, x) = a*t+1

which is not a solution of the PDE2

However, both differential equations are equal, only the arguments are swapped around. Am I doing something wrong, or is this a bug?


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