The solution of the differential equation (x^2+y^2)dx=2xydy is

The solution of the differential equation (x^2+y^2)dx=2xydy is


1 Answers

Badiuddin askIITians.ismu Expert
148 Points
13 years ago

Dear pallavi


dy/dx = (x2+y2)/2xy

let y=vx

 so dy/dx  = v + xdv/dx

put these value

v + xdv/dx = (x2+(xv)2)/2xvx

v + xdv/dx  =(1+v2)/2v

 x dv/dx  = (1+v2)/2v   -v

x dv/dx    = (1- v2)/2v

 2v/(1- v2)  dv   =  dx/x

now let 1-v2 =t

           -2vdv =dt

 -dt/t  =dx/x

 -lnt = lnx + C

 where C is constant

  t =c/x

 or  1-v2   =C/x

or  1-(y/x)2  =C/x

 (y/x)=1 -C/x

  y2 = x2 -Cx

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