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

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

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2y(dy)/(dx)=x(y^2+1),y(2)=0

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

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

Solution steps

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

Solve separable ODE:

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

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

\int \frac{10 x ^{2} - 9 x + 24}{x ^{3} + 4 x} d x

\frac{d y}{d x} = sin (4 x)

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

\int 9 x^{2} sec (x^{3}) tan (x^{3}) d x

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