Question

For problem given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation:
$straight y space equals space straight x space sin space 3 straight x$ : $fraction numerator straight d squared straight y over denominator dx squared end fraction plus 9 straight y minus 6 space cos space 3 straight x space equals space 0$

Solution

The given differential equation is

straight y equals space straight x space sin space 3 straight x

...(1)

rightwards double arrow

dy over dx space equals space straight x space cos 3 straight x space. space 3 space plus space sin space 3 straight x

and

fraction numerator straight d squared straight y over denominator dx squared end fraction equals 3 space open curly brackets straight x left parenthesis negative sin space 3 straight x space.3 right parenthesis plus cos space 3 straight x close curly brackets space plus space cos space 3 straight x. space 3

fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative 9 space straight x space sin 3 straight x space plus space 6 space cos space 3 straight x

fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative 9 straight y plus 6 space cos space 3 straight x

open square brackets because space of space left parenthesis 1 right parenthesis close square brackets

fraction numerator straight d squared straight y over denominator dx squared end fraction plus 9 straight y minus 6 space cos space 3 straight x space equals space 0.

Hence the result.

Some More Questions From Vector Algebra Chapter

For Daily Free Study Material Join wiredfaculty