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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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