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