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(dy)/(dx)=(y-x)/(y+x)...

(dy)/(dx)=(y-x)/(y+x)

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(dy)/(dx)=(y-x)/(x+y)

If (dy)/(dx)=(y-x+2)/(y-x+1), then

(dy)/(dx)=(y(y+x))/(x(y-x))

(dy)/(dx)=(y)/(x)+cot""(y)/(x)

(dy)/(dx)=(y)/(x)-tan""(y)/(x)

(dy)/(dx)=(y)/(x)+tan((y)/(x))

(dy)/(dx)=(y)/(x)+x sin((y)/(x))

(dy)/(dx)=(x+y)/(x-y)

The solution of (dy)/(dx)=(y)/(x)+(tan)(y)/(x) is :

Solve the equation (dy)/(dx)=(y)/(x)-(y^(2))/(x^(2))