differential equations – How to solve this mixed partial derivative with ndsolve?

I tried the following mixed pde but although I get an interpolation function – I still can’t plot it.

sol1 = NDSolve[{D[u[x, t], t, x] + Exp[x*t]*u[x, t] == 0, 
   u[-25, t] == Exp[-100], u[25, t] == Exp[-100], u[x, 0] == Exp[0]}, 
  u, {x, -25, 25}, {t, 0, 25}]

Plot3D[sol1, {x, -25, 25}, {t, 0, 25}]

I remember using the exponential trick for the boundaries. Is there another trick to get a solution for this?