ODE
\[ y'(x)^2+2 y'(x)+x=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.165972 (sec), leaf count = 47
\[\left \{\left \{y(x)\to -\frac {2}{3} (1-x)^{3/2}-x+c_1\right \},\left \{y(x)\to \frac {2}{3} (1-x)^{3/2}-x+c_1\right \}\right \}\]
Maple ✓
cpu = 0.03 (sec), leaf count = 35
\[\left [y \left (x \right ) = -x +\frac {2 \left (1-x \right )^{\frac {3}{2}}}{3}+\textit {\_C1}, y \left (x \right ) = -x -\frac {2 \left (1-x \right )^{\frac {3}{2}}}{3}+\textit {\_C1}\right ]\] Mathematica raw input
DSolve[x + 2*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-2*(1 - x)^(3/2))/3 - x + C[1]}, {y[x] -> (2*(1 - x)^(3/2))/3 - x + C[1]}}
Maple raw input
dsolve(diff(y(x),x)^2+2*diff(y(x),x)+x = 0, y(x))
Maple raw output
[y(x) = -x+2/3*(1-x)^(3/2)+_C1, y(x) = -x-2/3*(1-x)^(3/2)+_C1]