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

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

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

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

y = 2 tan (\frac{x}{2}) + c_{1}, y = - 2 tan (\frac{x}{2}) + c_{1}

Solution steps

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

Solve separable ODE:

y = 2 tan (\frac{x}{2}) + c_{1}, y = - 2 tan (\frac{x}{2}) + c_{1}

y = 2 tan (\frac{x}{2}) + c_{1}, y = - 2 tan (\frac{x}{2}) + c_{1}

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