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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d P}{d t} = 7 Pt, P (1) = 5

y^{^{'}} = y sec (x)

\frac{d y}{d x} = y + \frac{y}{x ln ( x )}

\frac{d y}{d t} + 20 y = 24, y = \frac{6}{5} - \frac{6}{5} e^{- 20 t}

d y = 1 - 4 y^{2} d x

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