Differential Equations

Question

Solve:
$dy over dx space equals straight y over straight x plus tan straight y over straight x open parentheses 0 less than straight y over straight x less than straight pi over 2 close parentheses$

Solution

The given differential equation is
$dy over dx space equals space straight y over straight x plus tan straight y over straight x space space space space space space space space space space space space open parentheses 0 less than straight y over straight x less than straight pi over 2 close parentheses$ ...(1)
Put y = v x so that $dy over dx equals straight v plus straight x dv over dx$
$therefore space space space space from space left parenthesis 1 right parenthesis comma space space straight v plus straight x dv over dx space equals space straight v plus tan space straight v space space or space space space straight x dv over dx space equals space tan space straight v space space or space space space fraction numerator 1 over denominator tan space straight v end fraction dv space equals space dx over straight x$
or $integral cot space straight v space dv space equals space integral dx over straight x$
or $log space open vertical bar sin space straight v close vertical bar space equals space log space open vertical bar straight x close vertical bar space plus space log space open vertical bar straight c close vertical bar space space or space space space log space open vertical bar sin space straight v close vertical bar space equals space log space open vertical bar cx close vertical bar$
or $sin space straight v space equals space cx space space space space or space space space space space sin straight y over straight x space equals space space straight c space straight x space is space the space required space solution. space$

For Daily Free Study Material Join wiredfaculty

Differential Equations

Solve:
$dy over dx space equals straight y over straight x plus tan straight y over straight x open parentheses 0 less than straight y over straight x less than straight pi over 2 close parentheses$

Some More Questions From Differential Equations Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction