+91-8076753736 [email protected]

-->

Differential Equations

Question

Wired Faculty App

Solve:
$straight x dy over dx minus straight y plus straight x space tan straight y over straight x equals 0$

Solution

The given differential equation is

straight x dy over dx minus straight y plus straight x space tan straight y over straight x space equals space 0

or

straight x dy over dx space equals space straight y minus straight x space tan straight y over straight x

or

dy over dx space equals space straight y over straight x minus tan straight y over straight x

Put y = v x so that

dy over dx space equals straight v plus straight x dv over dx

therefore space space space space space space space space straight v plus straight x dv over dx space equals straight v minus tan space straight v therefore space space space space space straight x dv over dx space equals space minus tan space straight v or space space space space space space space space space space space space space space fraction numerator 1 over denominator tan space straight v end fraction dv space equals space minus 1 over straight x dx therefore space space space space space space space space space space integral fraction numerator 1 over denominator tan space straight v end fraction dv space equals space minus integral 1 over straight x dx therefore space space space space space space space space space space log space open vertical bar sin space straight v close vertical bar space equals space minus log space open vertical bar straight x close vertical bar space plus space log space open vertical bar straight c close vertical bar or space space space space space space space space space space space space log space open vertical bar straight x space space sinv close vertical bar space equals space log space open vertical bar straight c close vertical bar therefore space space space space space space space space space space space space space straight x space space sin space straight v space equals space straight c or space space space space space space space space space space space space space space space space straight x space sin space straight y over straight x space equals space straight c space is space the space required space solution. space

Some More Questions From Differential Equations Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation