Find all separable exponential solutions of:
a) u_tt= u_xx - 4 u_x + 2u
I have
u(x,t) = X(x)T(t)
X(x) = Ce^ax
X'(x) = aCe^ax
X''(x) = a^2Ce^ax
X''T-4X'+2X=0
= T(X''-4X'+2X)=0
= Ce^ax(a^2-4a+2)
b) u_xx + u_yy=0
u(x.y) = X(x)Y(y)
X''/X = -Y''/Y
X(x) = Ce^ax
not sure from here.
Thanks