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

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

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

If (dy)/(dx)=(y+xtan(y)/(x))/(x) then sin (y)/(x)=

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

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

solve x(dy)/(dx) - y + x sin ((y)/(x)) = 0

x(dy)/(dx) - y + x sin ((y)/(x)) = 0

x(dy)/(dx) - y + x sin ((y)/(x)) = 0

x (dy)/(dx)-y+x sin (y/x)=0

(dy/dx)+(y/x)=sin x^(2)