Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
Estevez Mansfield Clarkson equation. Solve for \(u(x,y,t)\) \[ u_{tyyy} + \beta u_y u_{yt} + \beta u_{yy} u_t + u_{tt} = 0 \]
Mathematica ✓
ClearAll["Global`*"]; pde = D[D[u[x, y, t], t], {y, 3}] + beta*D[u[x, y, t], y]*D[D[u[x, y, t], y], t] + beta*D[u[x, y, t], {y, 2}]*D[u[x, y, t], t] + D[u[x, y, t], {t, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y, t], {x, y, t}], 60*10]];
\[\left \{\left \{u(x,y,t)\to \frac {6 c_1(x) \tanh \left (-4 t (c_1(x)){}^3+y c_1(x)+c_3(x)\right )}{\beta }+c_4(x)\right \}\right \}\]
Maple ✓
restart; beta='beta'; pde := diff(u(x,y,t),t,y,y,y)+ beta*diff(u(x,y,t),y)*diff(u(x,y,t),y,t) + beta*diff(u(x,y,t),y$2)*diff(u(x,y,t),t) + diff(u(x,y,t),t$2)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y,t))),output='realtime'));
\[u \left (x , y , t\right ) = \frac {6 c_{3} \tanh \left (-4 c_{3}^{3} t +c_{2} x +c_{3} y +c_{1}\right )}{\beta }+c_{5}\]
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