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Solution :

`(1+y^2)(1+logx)dx+xdy = 0`<br>
`=>(1+logx)/xdx = -dy/(1+y^2)`<br>
Now, integrating both sides,<br>
`int (1+logx)/xdx = - int dy/(1+y^2)`<br>
Let, `1+logx = t => 1/x dx = dt`<br>
`=> int tdt = -int dy/(1+y^2)`<br>
`=>t^2/2 = tan^-1y+c`<br>
`=>(1+logx)^2/2+tan^-1y = c`, which is the required solution.<br>Related Video

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