Possible Duplicate:
Simplifying PDE
I have a pde:
$u_{tt}-7u_{xx}-u_{x}=0$
IC:
$u(x,0) = x - x^2 $ $u_t(x,0) = 0$
BC:
$u(0,t) = 0 $ $u(L,t) = \sin(\pi t / 2)$
$t_\mathrm{last} = 2$ $L = 1$
I was simplifying it using next formulas:
$u(x,t)=e^{\lambda x + \mu t}\ V(x,t) $ $u_{x} = e^{\lambda x + \mu t}(\lambda V + V_{x})$ $u_{xx} = e^{\lambda x + \mu t}(\lambda^{2} V + 2\lambda V_{x} + V_{xx})$ $u_{tt} = e^{\lambda x + \mu t}(\mu^{2} V + 2\mu V_{t} + V_{tt})$
After that I've got: $V_{tt}-7V_{xx}-\frac{3}{28}V=0 $ Help please: IC and BC must change, but how to change them? What will be new IC\BC?