Determine if the following PDEs are separable If it is not s

Determine if the following PDEs are separable. If it is not separable, give a brief explanation on why. u_t - u_x = u_xx u_tt - u_t = u_xx u_tt + e^xt u_xx = 0

Solution

a) ut - ux = uxx

The differential equation is non-seperable

b) utt - ut = uxx

The differential equation is non-seperable

c) The differential equation is seperable

utt = -e^(xt) uxx

Taking the power of e^(t) in the LHS we get

e^(-t)utt = -e^(x) uxx

Hence the differential equation is seperable in nature