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

The solution for sqrt((1+x^2)/(1+y))(dy)/(dx)=-x is y=(1+x^2+c_{1}^2)/4-(c_{1}sqrt(x^2+1))/2-1

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

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

y = \frac{1 + x ^{2} + c _{1}^{2}}{4} - \frac{c _{1} x ^{2} + 1}{2} - 1

Solution steps

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

Solve separable ODE:

y = \frac{1 + x ^{2} + c _{1}^{2}}{4} - \frac{c _{1} x ^{2} + 1}{2} - 1

y = \frac{1 + x ^{2} + c _{1}^{2}}{4} - \frac{c _{1} x ^{2} + 1}{2} - 1

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

\frac{d x}{d t} = - \frac{x}{25}

\frac{d y}{d t} = e^{6 y + 4 t}, y (0) = 14

y^{^{'}} = x^{2} y^{2} - y^{2} + x^{2} - 1

x^{2} \frac{d y}{d x} = 5 y

What is the solution for sqrt((1+x^2)/(1+y))(dy)/(dx)=-x ?
The solution for sqrt((1+x^2)/(1+y))(dy)/(dx)=-x is y=(1+x^2+c_{1}^2)/4-(c_{1}sqrt(x^2+1))/2-1