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

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

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

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

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

Solution steps

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

Solve using substitution:

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

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

\int_{0}^{1} (2 x + 1)^{3} d x

f (x) = 3 x + 7, (3, 4)

\frac{1}{s ( s ^{2} + 2 s + 2 )}

(x - 2)^{2} (x + 4)

x^{\frac{9}{6}}, 2

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