The conditions are evidently incomplete:
In[8]:= DSolve[{D[y[x, t], {x, 2}] + 3 D[y[x, t], x] + 2 y[x, t] ==
E^t, y[x, 0] == 1, D[y[x, 0], x] == 0}, y[x, t], {x, t}]
During evaluation of In[8]:= DSolve::bvnr: For some branches of the general solution, the given boundary conditions do not restrict the existing freedom in the general solution. >>
During evaluation of In[8]:= DSolve::bvsing: Unable to resolve some of the arbitrary constants in the general solution using the given boundary conditions. It is possible that some of the conditions have been specified at a singular point for the equation. >>
Out[8]= {{y[x, t] ->
1/2 E^(-2 x) (E^(t + 2 x) + 2 C[1][t] + 2 E^x C[2][t])}}
