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From Mathematica symbolic PDE document.
Solve for \(u(x,t)\) \[ \frac {\partial ^3 u}{\partial x^3} + \frac {\partial u}{\partial t}- 6 u(x,t) \frac {\partial u}{\partial x} = 0 \]
Reference https://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equation
Mathematica ✓
ClearAll[u, x, t]; pde = D[u[x, t], {x, 3}] + D[u[x, t], {t}] - 6*u[x, t]*D[u[x, t], {x}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]];
\[ \left \{\left \{u(x,t)\to \frac {12 c_1^3 \tanh ^2\left (c_2 t+c_1 x+c_3\right )-8 c_1^3+c_2}{6 c_1}\right \}\right \} \]
Maple ✓
x:='x'; y:='y';u:='u'; pde:= diff(u(x,t),x$3)+ diff(u(x,t),t)-6*u(x,t)* diff(u(x,t),x)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,t))),output='realtime'));
\[ u \left ( x,t \right ) =2\,{{\it \_C2}}^{2} \left ( \tanh \left ( {\it \_C2}\,x+{\it \_C3}\,t+{\it \_C1} \right ) \right ) ^{2}-1/6\,{\frac {8\,{{\it \_C2}}^{3}-{\it \_C3}}{{\it \_C2}}} \]