What is the solution for y^'*sqrt(1+x^2)=xy^2 ?

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

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y^'*sqrt(1+x^2)=xy^2

y^{^{'}} \cdot 1 + x^{2} = x y^{2}

y = - \frac{x ^{2} + 1 - c _{1}}{x ^{2} + 1 - c _{1}^{2}}

Solution steps

y^{'} (x) \cdot 1 + x^{2} = x y^{2}

Solve separable ODE:

y = - \frac{x ^{2} + 1 - c _{1}}{x ^{2} + 1 - c _{1}^{2}}

y = - \frac{x ^{2} + 1 - c _{1}}{x ^{2} + 1 - c _{1}^{2}}

\frac{d}{d x} (7 + 5 x)

f (x) = \frac{1}{x + 4}

{\frac{4 s}{4 s ^{2} + 1}}

x \to 0 lim (2 x - x^{2} - x^{3})

\int cos (x^{5}) d x

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