Partial Differential Equations : Linear & Quasi-Linear PDEs

Study concepts, example questions & explanations for Partial Differential Equations

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Example Questions

Example Question #1 : First Order Pd Es

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:

Possible Answers:

True

False

Correct answer:

True

Explanation:

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

 is some function 

From here, differential  with respect to  and .

Next eliminate  as it is an arbitrary function.

This leads to the result,

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.

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