Linear & Quasi-Linear PDEs

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Differential Equations › Linear & Quasi-Linear PDEs

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Determine if the statement is true or false:

If the -axis is the axis of symmetry and a surface is revolving around it and is an arbitrary function, then the partial differential equation associated with that said surface, satisfies the equation:

True

False

Explanation

To determine the truth of this statement, assume the following.

is some function

From here, differential with respect to and .

$\\frac{dz}{dx}=2x\cdot f'(u) \\\frac{dz}{dy}=2y\cdot f'(u)$

Next eliminate as it is an arbitrary function.

This leads to the result,

$y\cdot \frac{dz}{dx}-x\cdot \frac{dy}{dz}=0$

Therefore, the statement,

is true.