What is the solution for xy^2+sqrt(1+x^2)(dy)/(dx)=0 ?

The solution for xy^2+sqrt(1+x^2)(dy)/(dx)=0 is y=-(sqrt(x^2+1)+c_{1})/(c_{1)^2-x^2-1}

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xy^2+sqrt(1+x^2)(dy)/(dx)=0

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

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

Solution steps

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

Solve separable ODE:

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

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

f (x) = \frac{6}{x}

(10, x), (8, 10)

y = \frac{6 x ^{2} + 8 x + 6}{x}

x + 2, - 1, 2, 5

What is the solution for xy^2+sqrt(1+x^2)(dy)/(dx)=0 ?
The solution for xy^2+sqrt(1+x^2)(dy)/(dx)=0 is y=-(sqrt(x^2+1)+c_{1})/(c_{1)^2-x^2-1}