What is the solution for (dy)/(dt)=-t/(2y) ?

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

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(dy)/(dt)=-t/(2y)

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

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

Solution steps

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

Solve separable ODE:

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

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

(3 x y^{2} - x^{3}) \frac{d y}{d x} = 3 y^{3} - x^{2} y

\frac{d y}{d x} = \frac{sin ( 3 x )}{cos ( 4 y )}

y^{^{'}} = \frac{x ^{3}}{y}

\frac{d y}{d x} = e^{- y} (2 x - 4)

4 y^{^{'}} + 6 y = 120, y (0) = 1

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