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

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

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(dy)/(dx)=-x/(2y)

\frac{d y}{d x} = - \frac{x}{2 y}

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

Solution steps

\frac{d y}{d x} = - \frac{x}{2 y}

Solve separable ODE:

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

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

\frac{d y}{d s} = \frac{s}{y ^{2}}

2 y^{^{'}} + 10 y = 3 u, y (0) = - 2

2 y^{^{'}} + y = 0, y (0) = e^{\frac{- x}{2}}

y^{^{'}} = \frac{x ^{2} - 6}{y ^{2}}, y (0) = 2

\frac{d y}{d x} = \frac{x ^{2}}{x ^{2} ( 3 y ^{2} + 1 )}, y (1) = 4

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