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Solve: y^(4)dx+2xy^(3)dy=(ydx-xdy)/(x^(3...

Solve: `y^(4)dx+2xy^(3)dy=(ydx-xdy)/(x^(3)y^(3))`

Text Solution

Verified by Experts

We can rewrite the given equation as
`y^(4)dx+2xy^(3)dy+1/(xy^(3))(xdy-ydx)/(x^(2))=0`
`rArr xy^(7)dx+2x^(2)y^(6)dy+d(y/x)=0`
`rArr x^(2)y^(6)dx+2x^(3)y^(5)dy+x/yd(y/x)=0`
`rArr 1/3(3x^(2)y^(6)+6x^(3)y^(5)dy)+(d(y//x))/(y//x)=0`
`rArr 1/3intd(x^(3)y^(6))+int(d(x//y)/(y//x))=0`
`rArr (x^(3)y^(6))/(3)+log_(e)y/x=c`
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