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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

cos (x) d y + (y sin (x) - cos^{4} (x)) d x = 0

f (x) = x + 2 sin (x)

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

2 x y d x + x^{2} d y = 0

x \to 3 + lim (x^{2} + 2 x)

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