2.15.12 Dym equation \(u_t =u^3 u_{xxx}\)

problem number 121

Added December 27, 2018.

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

Dym equation. Solve for \(u(x,t)\) \[ u_t =u^3 u_{xxx} \]

Mathematica


Failed

Maple


\[u \left (x , t\right ) = \frac {\RootOf \left (c_{3}+x -\left (\int _{}^{\mathit {\_Z}}\frac {1}{\RootOf \left (c_{2}+2 \left (\int _{}^{\mathit {\_Z}}\frac {\mathit {\_h}}{\mathit {\_h}^{2}+2 2^{\frac {1}{3}} \left (-\mathit {\_c}_{1}^{2}\right )^{\frac {1}{3}} \RootOf \left (c_{1} 2^{\frac {1}{3}} \left (-\mathit {\_c}_{1}^{2}\right )^{\frac {1}{3}} \mathit {\_h} \AiryBi \left (\mathit {\_Z} \right )+2 c_{1} \mathit {\_c}_{1} \AiryBi \left (1, \mathit {\_Z}\right )+2^{\frac {1}{3}} \left (-\mathit {\_c}_{1}^{2}\right )^{\frac {1}{3}} \mathit {\_h} \AiryAi \left (\mathit {\_Z} \right )+2 \mathit {\_c}_{1} \AiryAi \left (1, \mathit {\_Z}\right )\right )}d\mathit {\_h} \right )-\ln \left (\mathit {\_f} \right )\right )}d\mathit {\_f} \right )\right )}{\left (-3 t \mathit {\_c}_{1}+c_{4}\right )^{\frac {1}{3}}}\] has RootOf

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