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

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

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

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

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

Solution steps

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

Solve Bernoulli ODE:

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

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

f (x) = c y^{- 5}

\frac{\partial}{\partial x} (ln (k t - m x))

\frac{\partial}{\partial x} (\frac{x}{y ^{2}} - \frac{y}{x ^{2}})

(x^{2})^{- 1}

\frac{d}{d x} (\frac{1}{( x ^{2} - 1 ) ( x ^{2} + x + 1 )})

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