IGNOU MTE 8 2018 - Find the complete integral of the equation z2 x1 x2 x3.

Question

Find the complete integral of the equation
$(\frac{\partial z}{\partial x1})(\frac{\partial z}{\partial x^2})(\frac{\partial z}{\partial xz}) =$ z² x₁x₂ x_3.

13 Feb 2018

Answer :

Word Count : 376

To solve the equation: \[ \left( \frac{\partial z}{\partial x_1} \right) \left( \frac{\partial z}{\partial x_2} \right) \left( \frac{\partial z}{\partial x_3} \right) = z^2 x_1 x_2 x_3 \] We will approach it step by step. ### Step 1: Separate the equation We can simplify the equation by recognizing that it's a product of partial derivatives with respect to different variables. We start by rewriting it as: \[ \frac{\partial z}{\partial x_1} \cdot \frac{\partial z}{\partial x_2} \cdot \frac{\partial z}{\partial x_3} = z^2 x_1 x_2 x_3 \] ### Step 2: Assume a separable solution for $ z $ We assume that the solution $ z $ can be written in

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