+91-8076753736 [email protected]

-->

Differential Equations

Question

Wired Faculty App

Solve the following differential equation:
$sin space straight x space dy over dx plus straight y space cosx space equals space cos space straight x space sin squared straight x$

Solution

The given differential equations is

sinx dy over dx plus straight y space cosx space equals space cosx space sin squared straight x

or

dy over dx plus straight y space cotx space equals space cos space straight x space sinx

Comparing it with

dy over dx plus Py space equals space straight Q comma

we get.

straight P space equals cot space straight x comma space space space straight Q space equals space space cosx space sinx

therefore space space space space integral space straight P space dx space equals space integral space cot space straight x space dx space equals space log space sinx

therefore space space space straight I. straight F. space equals space straight e to the power of integral straight P space dx end exponent space equals space straight e to the power of log space sinx end exponent space equals space sin space straight x

therefore space space space solution space of space differential space equation space is

straight y. space sinx space space equals space integral space cosx. space sinx. space sinx space dx space plus space straight c space space space space open square brackets because space space straight y space straight e to the power of integral straight P space dx 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 equals space integral sin squared straight x space cosx space dx plus straight c

or

straight y space sinx space equals space fraction numerator sin cubed straight x over denominator 3 end fraction plus straight c

or

straight y equals 1 third sin squared straight x plus straight c space cosec space straight x.

Some More Questions From Differential Equations Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation