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" 4."x^(2)(dy)/(dx)-xy=1+cos((y)/(x))...

" 4."x^(2)(dy)/(dx)-xy=1+cos((y)/(x))

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Solve the following differential equation x^(2)(dy)/(dx)-xy=1+cos((y)/(x)),x!=0

The solution of (x^(2)dy)/(dx)-xy=1+cos((y)/(x)) is

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

The solution of the differential equation x^2(dy)/(dx)-xy=1+cos""(y)/x is

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