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 x1 x2 x3.

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 a form separable in terms of \( x_1 \), \( x_2 \), and \( x_3 \), such as: \[ z = f(x_1) g(x_2)
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Solve the following differential equations

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Classify the following as true or false giving reasons for your answers..
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