Q9Mathematics I

Question

Solve $(D^{4} + a^{4}) y = 0, a > 0$ .

Answer 1

The divergence of any vector field $f$ is strictly defined as the mathematical sum of its unmixed first-order partial derivatives: $\nabla \cdot f = \frac{\partial f _{x}}{\partial x} + \frac{\partial f _{y}}{\partial y} + \frac{\partial f _{z}}{\partial z}$ .

div f = \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial y} (- 2 x y^{2} z) + \frac{\partial}{\partial z} (3 x^{2} z) = 2 x y - 4 x y z + 3 x^{2}

Substituting the exact numerical coordinates $x = 3$ , $y = - 1$ , and $z = - 2$ directly into this derived polynomial yields $(- 6) - (24) + (27) = - 3$ .

Q9Mathematics I

Question

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