2.16.7 Linear PDE, initial conditions at \(t=t_0\)

problem number 146

Added December 20, 2018.

Example 26, Taken from https://www.mapleprimes.com/posts/209970-Exact-Solutions-For-PDE-And-Boundary--Initial-Conditions-2018

Solve for \(w(x_1,x_2,x_3,t)\)

\[ \frac {\partial w}{\partial t} = \frac {\partial w^2}{\partial x_1 x_2} + \frac {\partial w^2}{\partial x_1 x_3} + \frac {\partial w^2}{\partial x_3^2} + \frac {\partial w^2}{\partial x_2 x_3} \]

With initial condition \(w(x_1,x_2,x_3,t_0) = e^{x_1} +x_2 -3 x_3\)

Mathematica


\[\left \{\left \{w(\text {x1},\text {x2},\text {x3},t)\to e^{\text {x1}}+\text {x2}-3 \text {x3}\right \}\right \}\]

Maple


\[w \left (\mathit {x1} , \mathit {x2} , \mathit {x3} , t\right ) = \mathit {x2} -3 \mathit {x3} +{\mathrm e}^{\mathit {x1}}\]

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