+91-8076753736 [email protected]

-->

Differential Equations

Question

Wired Faculty App

Solve:
$dy over dx plus 2 straight y space equals space sin space 3 straight x$

Solution

The given differential equation is

dy over dx plus 2 straight y space equals sin space 3 straight x

Comparing it with

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

P = 2, Q = sin 3x

integral straight P space dx space equals space integral 2 space dx space equals space 2 straight x

straight I. straight F. space equals space straight e to the power of integral Pdx end exponent space equals space straight e to the power of 2 straight x end exponent

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

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 space space space space space or space space space straight y space straight e to the power of 2 straight x end exponent space equals space integral straight e to the power of 2 straight x end exponent space sin space 3 straight x space dx space plus straight c

therefore space space space space ye to the power of 2 straight x end exponent space equals space fraction numerator 1 over denominator square root of 4 plus 9 end root end fraction space straight e to the power of 2 straight x end exponent space sin space open parentheses 3 straight x minus tan to the power of negative 1 end exponent 3 over 2 close parentheses space plus straight c

open square brackets because space space space integral straight e to the power of ax space sin space bx space dx space equals space fraction numerator 1 over denominator square root of straight a squared plus straight b squared end root end fraction straight e to the power of ax space sin open parentheses bx minus tan to the power of negative 1 end exponent straight b over straight a close parentheses close square brackets

or

straight y equals space fraction numerator 1 over denominator square root of 13 end fraction sin space open parentheses 3 straight x minus tan to the power of negative 1 end exponent 3 over 2 close parentheses plus space ce to the power of negative 2 straight x end exponent

which is required solution.

Some More Questions From Differential Equations Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation