What is the solution for ((1+x^2)dy)/(dx)-(1+y^2)=0 ?

The solution for ((1+x^2)dy)/(dx)-(1+y^2)=0 is y=tan(arctan(x)+c_{1})

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((1+x^2)dy)/(dx)-(1+y^2)=0

\frac{( 1 + x ^{2} ) d y}{d x} - (1 + y^{2}) = 0

y = tan (arctan (x) + c_{1})

Solution steps

\frac{( 1 + x ^{2} ) d y}{d x} - (1 + y^{2}) = 0

Solve separable ODE:

y = tan (arctan (x) + c_{1})

y = tan (arctan (x) + c_{1})

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\frac{y d y + x d x}{2 1 + x y} = 0

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What is the solution for ((1+x^2)dy)/(dx)-(1+y^2)=0 ?
The solution for ((1+x^2)dy)/(dx)-(1+y^2)=0 is y=tan(arctan(x)+c_{1})