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pallavi pradeep bhardwaj Grade: 12
`        The solution of the differential equation (x^2+y^2)dx=2xydy is`
7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
```										Dear pallavi
(x^2+y^2)dx=2xydy
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)2  =1 -C/x
y2 = x2 -Cx
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin

```
7 years ago
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