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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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

\frac{d y}{d x} + (y - \frac{1}{y}) x = 0

\frac{d y}{d x} = - \frac{3}{8} x^{5} y^{8}

y^{^{'}} + y cos (x) = 6 cos (x), y (0) = 8

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