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 \cdot \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 \cdot \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

\frac{d}{d x} (in (x^{2} - 5))

y^{^{'}} = 1 - e^{x - y + 8}

\frac{5}{8 s}

x \to 3 + lim ((x^{2} - 9)^{x - 3})

\int \frac{t ^{2} + 8}{t ^{2} - 5 t + 6} d t

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}