Linear & Quasi-Linear PDEs Flashcards - Partial Differential Equations

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,

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:

is true.

Linear & Quasi-Linear PDEs - Partial Differential Equations

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:

Linear & Quasi-Linear PDEs - Partial Differential Equations

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:

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: