What is the solution for y^'= y/t-1/(y/t) ?

The solution for y^'= y/t-1/(y/t) is y=tsqrt(-2ln(t)+c_{1)},y=-tsqrt(-2ln(t)+c_{1)}

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y^'= y/t-1/(y/t)

y^{^{'}} = \frac{y}{t} - \frac{1}{\frac{y}{t}}

y = t - 2 ln (t) + c_{1}, y = - t - 2 ln (t) + c_{1}

Solution steps

y^{'} (t) = \frac{y}{t} - \frac{1}{\frac{y}{t}}

Solve Bernoulli ODE:

y = t - 2 ln (t) + c_{1}, y = - t - 2 ln (t) + c_{1}

y = t - 2 ln (t) + c_{1}, y = - t - 2 ln (t) + c_{1}

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What is the solution for y^'= y/t-1/(y/t) ?
The solution for y^'= y/t-1/(y/t) is y=tsqrt(-2ln(t)+c_{1)},y=-tsqrt(-2ln(t)+c_{1)}