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(i) x dy=(y+sqrt(x^(2)+y^(2)))dx (ii) ...

(i) `x dy=(y+sqrt(x^(2)+y^(2)))dx`
(ii) `y dx +xlog((y)/(x))dy-2x dy=0`

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x(dy)/(dx)=y+sqrt(x^(2)-y^(2))

x dy - y dx = sqrt(x^(2) + y^(2)) dx

x dy - y dx = sqrt(x^(2) + y^(2)) dx

Express x dy-y dx=sqrt(x^(2)+y^(2)) dx in the form F((y)/(x))=(dy)/(dx) .

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

solve x(dy)/(dx)-y=sqrt(x^(2)+y^(2))

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)