What is the solution for (ydy+xdx)/(2sqrt(1+xy))=0 ?

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

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(ydy+xdx)/(2sqrt(1+xy))=0

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{\partial}{\partial x} (4 x^{3} y^{\frac{1}{2}})

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 5)^{6})

x \to - 1 lim (\frac{x ^{2}}{x ^{3} - x})

\frac{\partial}{\partial x} (4 y^{2} x^{3})

\int_{0}^{1} (x + 1) (x^{2} + 2 x)^{5} d x

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