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?