Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • The general solution of the differential equation dy /dx =y tan x -y^2 sec x

The general solution of the differential equation dy /dx =y tan x -y^2 sec x

Answers (1)

best_answer

Solution:  We have ,

                 fracmathrmd ymathrmd x=y an x-y^2sec x

         Rightarrow      frac1y^2fracmathrmd ymathrmd x-frac1y an x=-sec x

           Putting       frac1y=vRightarrow -frac1y^2fracmathrmd ymathrmd x=fracmathrmd vmathrmd x.   We get

       Rightarrow       fracmathrmd vmathrmd x+ an xcdot v=sec x   Which is linear differential equation

               I.F=e^int an xdx=e^log sec x=sec x

      The solution is    vcdot sec x=int sec^2x dx+cRightarrow sec x =y(c+ an x).

Posted by

Deependra Verma

View full answer

Similar Questions

Latest Question