What is the solution for y^'=-(1+x+y)/(1+x) ?

The solution for y^'=-(1+x+y)/(1+x) is y=-x/(1+x)-(x^2)/(2(1+x))+(c_{1})/(1+x)

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y^'=-(1+x+y)/(1+x)

y^{^{'}} = - \frac{1 + x + y}{1 + x}

y = - \frac{x}{1 + x} - \frac{x ^{2}}{2 ( 1 + x )} + \frac{c _{1}}{1 + x}

Solution steps

y^{'} (x) = - \frac{1 + x + y}{1 + x}

Solve linear ODE:

y = - \frac{x}{1 + x} - \frac{x ^{2}}{2 ( 1 + x )} + \frac{c _{1}}{1 + x}

y = - \frac{x}{1 + x} - \frac{x ^{2}}{2 ( 1 + x )} + \frac{c _{1}}{1 + x}

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What is the solution for y^'=-(1+x+y)/(1+x) ?
The solution for y^'=-(1+x+y)/(1+x) is y=-x/(1+x)-(x^2)/(2(1+x))+(c_{1})/(1+x)