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

The solution for xy(dy)/(dx)=1+y^2 is y=sqrt(c_{1)x^2-1},y=-sqrt(c_{1)x^2-1}

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

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

y = c_{1} x^{2} - 1, y = - c_{1} x^{2} - 1

Solution steps

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

Solve separable ODE:

y = c_{1} x^{2} - 1, y = - c_{1} x^{2} - 1

y = c_{1} x^{2} - 1, y = - c_{1} x^{2} - 1

y^{^{'}} - \frac{2}{x} y = \frac{y ^{5}}{x ^{2}}

\frac{d}{d x} (\frac{lo g _{e} ( x )}{x ^{2}})

y^{^{''}} - 2 y^{^{'}} - 3 y = 0

f (t) = t

x \to 2 lim (\frac{x}{x + 1})

What is the solution for xy(dy)/(dx)=1+y^2 ?
The solution for xy(dy)/(dx)=1+y^2 is y=sqrt(c_{1)x^2-1},y=-sqrt(c_{1)x^2-1}