+91-8076753736 [email protected]

-->

Differential Equations

Question

Wired Faculty App

Solve:
$dy over dx plus straight y space cotx space equals space straight x squared space cotx space plus space 2 straight x$

Solution

The given differential equation is

dy over dx plus straight y space cotx space equals straight x squared cotx space plus space 2 straight x

Comparing it with

dy over dx plus Py space equals space straight Q comma space space we space get comma

P = cot x,

straight Q space equals straight x squared space cot space straight x space plus space 2 straight x

integral straight P space dx space equals space integral cot space straight x space dx space equals space log space sinx. space straight e to the power of integral Pdx end exponent space equals space straight e to the power of log space sinx end exponent space equals space sin space straight x space

therefore

solution of differential equation is

straight y. space sin space straight x space equals space integral left parenthesis straight x squared space cot space straight x space plus space 2 straight x right parenthesis space sinx space dx space plus space straight c space space space space space open square brackets straight y space straight e to the power of integral Pdx end exponent space equals space integral straight Q space straight e to the power of integral straight P space dx end exponent dx plus straight c close square brackets

or

straight y. space sinx space space equals space integral left parenthesis straight x squared space cosx space plus 2 straight x space sin space straight x right parenthesis space dx space plus space straight c

or space space space straight y space sin space straight x space equals space integral space straight x squared space cosx space dx space space plus integral space 2 space straight x space sinx space dx space plus space straight c

or space space space straight y space sinx space minus straight x squared space sinx space minus space integral 2 straight x space sinx space dx space plus space integral 2 straight x space sinx space dx plus straight c or space space space straight y space sinx space space equals space straight x squared sin space straight x space plus space straight c

Some More Questions From Differential Equations Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation