Question

Which of the following differential equations has y = x as one of its particular solution?
$fraction numerator straight d squared straight y over denominator dx squared end fraction minus straight x squared dy over dx plus straight x space straight y space equals straight x$
$fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x dy over dx plus straight x space straight y space equals space straight x$
$fraction numerator straight d squared straight y over denominator dx squared end fraction minus straight x squared dy over dx plus straight x space straight y space equals space 0$
$fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x dy over dx plus xy space equals space 0$

Solution

fraction numerator straight d squared straight y over denominator dx squared end fraction minus straight x squared dy over dx plus straight x space straight y space equals space 0

Here y = x
$therefore space space space space space space space space space space space space space space space space space space space space dy over dx space equals space 1 comma space space space space fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space 0$
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$therefore space space space left parenthesis straight C right parenthesis space is space correct space answer.$

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Vector Algebra

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Vector Algebra

Which of the following differential equations has y = x as one of its particular solution?