2.15.29 Thomas equation \( u_{xy} + \alpha u_x + \beta u_y+ \nu u_x u_y =0\)

problem number 138

Added December 27, 2018.

Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations

Thomas equation. Solve for \(u(x,t)\) \[ u_{xy} + \alpha u_x + \beta u_y+ \nu u_x u_y =0 \]

Mathematica


Failed

Maple


\[u \left (x , y\right ) = \frac {-2 \alpha y -2 \beta x -\ln \left (\frac {\alpha ^{2}-2 \alpha \beta +\beta ^{2}-4 \mathit {\_c}_{1} \nu }{\left (c_{1} {\mathrm e}^{\left (x -y \right ) \sqrt {\alpha ^{2}-2 \alpha \beta +\beta ^{2}-4 \mathit {\_c}_{1} \nu }}-c_{2}\right )^{2} \nu ^{2}}\right )-\ln \left (\frac {\alpha ^{2}+2 \alpha \beta +\beta ^{2}-4 \mathit {\_c}_{1} \nu }{\left (c_{3} {\mathrm e}^{\left (x +y \right ) \sqrt {\alpha ^{2}+2 \alpha \beta +\beta ^{2}-4 \mathit {\_c}_{1} \nu }}-c_{4}\right )^{2} \nu ^{2}}\right )+\left (-x +y \right ) \sqrt {\alpha ^{2}-2 \alpha \beta +\beta ^{2}-4 \mathit {\_c}_{1} \nu }+\left (-x -y \right ) \sqrt {\alpha ^{2}+2 \alpha \beta +\beta ^{2}-4 \mathit {\_c}_{1} \nu }-4 \ln (2)}{2 \nu }\]

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