# Characteristic curves

Find a partial differential equation whose characteristic curves are the lines x-y=a, x+2y=b where a,b are arbitrary real constants.

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Problem:

Find a partial differential equation whose characteristic curves are the lines x-y=a, x+2y=b where a,b are arbitrary real constants.

Solution:

Since the partial differential equation (PDE) admits real characteristics, then it will be of hyperbolic type, that is:

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According to the theory, the corresponding equation of the characteristic curves is expressed by:

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#### Solution Summary

The expert finds a partial differential equation whose characteristic curve is a line.

$2.19