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(x^3+3x y^2)dx+(y^3+3x^2y)dy=0...

`(x^3+3x y^2)dx+(y^3+3x^2y)dy=0`

Text Solution

Verified by Experts

The correct Answer is:
`y^(4)+6x^(2)y^(2)+x^(2)=C`
`int(v^(3)+3v)/(v^(4)+6v^(2)+1)dv=-int1/xdx`
`rArr 1/4int(4v^(3)+12v)/(v^(4)+6v^(2)+1)dv=-int1/xdx`
`rArr 1/4log|v^(4)+6v^(2)+1|+log|x|=log|C_(1)|`
`rArr (v^(4)+6v^(2)+1)x^(4)=C_(1)^(4)=C` (say) `rArr y^(4)+6x^(2)y^(2)+x^(4)`=C.
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