Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • The solution of the differential equation dy/dx=siny+x/sin2y-xcosy is

The solution of the differential equation dy/dx=siny+x/sin2y-xcosy is

Answers (1)

best_answer

    Solution:      Here ,   

                      fracmathrmd ymathrmd x=sin y+x/sin 2y-xcos y

                    Put   sin y=tRightarrow cos ydy=dt

                   Rightarrow    (cos y)fracmathrmd ymathrmd x=sin y+x/2sin y-x

                  Rightarrow   fracmathrmd tmathrmd x=t+x/2t-x        Put  t=vxRightarrow fracmathrmd tmathrmd x=v+xfracmathrmd vmathrmd x

                    Rightarrow    x(fracmathrmd vmathrmd x)+v=vx+x/2vx-x=(v+1/2v-1)

                 herefore         xfracmathrmd vmathrmd x=(v+1/2v-1)-v=v+1-2v^2+v/2v-1

                  Rightarrow       (2v-1/-2v^2+2v+1)dv=dx/x

                  Rightarrow         sin^2y=x siny+x^2/2 +c

Posted by

Deependra Verma

View full answer

Similar Questions

Latest Question