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

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

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

Solution steps

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

Solve separable ODE:

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

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

f (x) = x^{2} - x + 5, at x = 5

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

\frac{d}{d x} (2 e^{- x^{2}} x - 2 e^{- x^{2}} x^{3})

f (x) = 2 x^{- \frac{3}{4}}

3 x - 5 x^{2}

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})