1. ## u_{xxx}+u_x=0

Find the general solution of u(x,y,z) of

$\displaystyle u_{xxx}+u_x=0$

Can I use this method $\displaystyle m^3+m=0$ for PDE?

Thanks.

$\displaystyle m(m^2+1)=0\Rightarrow m_1=0 \ \ m_2=\mathbf{i} \ \ m_3=-\mathbf{i}$

$\displaystyle u(x,y,z)=f(y,z)e^{0}+g(y,z)e^{x\mathbf{i}}\Rightar row u(x,y,z)=f(y,z)+g(y,z)e^{x\mathbf{i}}$

Pickslides I just read your other post and the answer is yes I am presuming.

2. Originally Posted by dwsmith
$\displaystyle u(x,y,z)=f(y,z)+g(y,z)e^{x\mathbf{i}}$

Pickslides I just read your other post and the answer is yes I am presuming.
Does it satisfy $\displaystyle \displaystyle u_{xxx}+u_x=0$ ?

3. Originally Posted by pickslides
Does it satisfy $\displaystyle \displaystyle u_{xxx}+u_x=0$ ?
Yes, $\displaystyle u_x=\mathbf{i}e^{x\mathbf{i}}g(y,z) \ , \ u_{xxx}=-\mathbf{i}e^{x\mathbf{i}}g(y,z)$

$\displaystyle -\mathbf{i}e^{x\mathbf{i}}g(y,z)+\mathbf{i}e^{x\mat hbf{i}}g(y,z)=0$