#### 2.16.6 $$w_t = w_{x_1 x_1} + w_{x_2 x_2} + w_{x_3 x_3}$$

problem number 145

Linear PDE, initial conditions at $$t=1$$. Solve for $$w(x_1,x_2,x_3,t)$$ $w_t = w_{x_1 x_1} + w_{x_2 x_2} + w_{x_3 x_3}$ With initial condition $$w(x_1,x_2,x_3,1) = e^a x_1^2 +x_2 x_3$$

Mathematica

$\left \{\left \{w(\text {x1},\text {x2},\text {x3},t)\to e^a \left (2 t+\text {x1}^2-2\right )+\text {x2} \text {x3}\right \}\right \}$

Maple

$w \left (\mathit {x1} , \mathit {x2} , \mathit {x3} , t\right ) = \mathit {x2} \mathit {x3} +\left (\mathit {x1}^{2}+2 t -2\right ) {\mathrm e}^{a}$

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