What is the solution for (dy)/(dt)=(1-ty^2)/(2t^2y) ?

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

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(dy)/(dt)=(1-ty^2)/(2t^2y)

\frac{d y}{d t} = \frac{1 - t y ^{2}}{2 t ^{2} y}

y = \frac{ln ( t ) + c _{1}}{t}, y = - \frac{ln ( t ) + c _{1}}{t}

Solution steps

\frac{d y}{d t} = \frac{1 - t y ^{2}}{2 t ^{2} y}

Solve Bernoulli ODE:

y = \frac{ln ( t ) + c _{1}}{t}, y = - \frac{ln ( t ) + c _{1}}{t}

y = \frac{ln ( t ) + c _{1}}{t}, y = - \frac{ln ( t ) + c _{1}}{t}

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