2.4.3 $u_t+u{u}_x=\mu u_{xx}$

problem number 86

From Mathematica symbolic PDE document.

viscous fluid flow with no initial conditions

Solve for $u(x,t)$ $$u_t+u{u}_x=\mu u_{xx}$$

Mathematica ✓

ClearAll["Global`*"]; 
pde =  D[u[x, t], {t}] + u[x, t]*D[u[x, t], {x}] == \[Mu]*D[u[x, t], {x, 2}]; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]];
 

$$\left\{\{u(x,t)\to -2c_1\mu \tanh (c_{2}t+c_{1}x+c_3)-\frac{c_2}{c_1}\}\right\}$$

Maple ✓

restart; 
interface(showassumed=0); 
pde := diff(u(x, t), t) + u(x, t)*diff(u(x, t), x) = mu* diff(u(x,t),x$2); 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde, u(x, t))),output='realtime'));
 

$$u(x,t)=\frac{-2c_2^2\mu \tanh (c_{3}t+c_{2}x+c_1)-c_3}{c_2}$$

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