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Question

Solve : y2+(x1y)dydx=0

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Solution

y2+(x1y)dydx=0
y2=(x1y)dydx
y3=(xy1)ydydx
y3=(1xy)dydx
11xydx=1y3dy
Solving LHS 11xydx
Substitute u=1yx
1yudu=1yduu
1ydu=1yduu
as 1/udu=ln|u|
1yln|u|=1yln|1yx|
1yln|1yx|+C1
solving RHS.1y3dy
y3dy
as x2dx=xn+1n+1+C
y3dy 12y2+C2
Hence, 1yln|1yx|+C1=12y2+C2
1yln|1yx|+12y2+C


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