2.15.13 Estevez Mansfield Clarkson \(u_{tyyy} + \beta u_y u_{yt} + \beta u_{yy} u_t + u_{tt} = 0\)

problem number 122

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


\[\left \{\left \{u(x,y,t)\to \frac {6 c_1(x) \tanh \left (-4 t (c_1(x)){}^3+y c_1(x)+c_3(x)\right )}{\beta }+c_4(x)\right \}\right \}\]

Maple


\[u \left (x , y , t\right ) = \frac {6 c_{3} \tanh \left (-4 c_{3}^{3} t +c_{2} x +c_{3} y +c_{1}\right )}{\beta }+c_{5}\]

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