+91-8076753736[email protected]
logo
logo
-->

Differential Equations

Question
CBSEENMA12033193
Wired Faculty App

Solve:
dy over dx plus straight y space equals space cos space 2 straight x


Solution

The given differential equation is dy over dx plus straight y space equals space cos space 2 straight x
Comparing it with dy over dx plus space straight P space straight y space equals space space straight Q comma space space we space get comma space space space straight P space equals space 1 comma space space space straight Q space equals space cos space 2 straight x
                 integral straight P space dx space equals space integral 1. space dx space equals space straight x comma space space space straight e to the power of integral straight P space dx end exponent space equals space straight e to the power of straight x
therefore solution of differential equation is
                              straight y. 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
or           straight y. straight e to the power of straight x space space equals space integral space cos space 2 straight x. space straight e to the power of straight x space dx plus space straight c space space space or space space straight y space straight e to the power of straight x space equals space fraction numerator 1 over denominator 1 plus 4 end fraction straight e to the power of straight x left parenthesis cos space 2 straight x plus 2 space sin space 2 straight x right parenthesis space plus straight c
or           straight y space equals space 1 fifth left parenthesis cos space straight x plus 2 space sin space 2 straight x right parenthesis space plus space straight c space straight e to the power of straight x

Some More Questions From Differential Equations Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation