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

The solution for (dy)/(dx)y=(tan(x))/(1+tan(x)) is

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = \frac{y}{x}, y = 1, x = 1

3 x \frac{d y}{d x} + y = \frac{8}{y ^{2}}

\frac{d y}{d x} + 5 \frac{d y}{d x} + 6 y = 0

\frac{d y}{d x} = \frac{18 x y}{( ln ( y ) ) ^{2}}

3 e^{7 x} \frac{d y}{d x} = - 49 (\frac{x}{y ^{2}}), y (0) = 1

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