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" 2."(dy)/(dx)=(1+y^(2))/(y^(3))...

" 2."(dy)/(dx)=(1+y^(2))/(y^(3))

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y(dy)/(dx)=1+y^(2)

Solve (dy)/(dx)=(1+y^(2))/(y^(3))

(dy)/(dx)+(1)/(2x)y=(x)/(y^(3))

Solve (dy)/(dx)=-((1+y^(2)))/(y)

(dy)/(dx)=(y^(3)-2x^(2)y)/(x^(3))

(dy)/(dx)+2y=3

If x^(2)+y^(2)=1 then (y'=(dy)/(dx),y''=(d^(2)y)/(dx^(2)))

(y-x(dy)/(dx))=3(1-x^(2)(dy)/(dx))

(dy)/(dx)=(x+y+1)/(2x+2y+3)

(dy)/(dx)=(x+y+1)/(2x+2y+3)