4.16.26 \(y'(x)^2+2 y'(x)+x=0\)

ODE
\[ y'(x)^2+2 y'(x)+x=0 \] ODE Classification

[_quadrature]

Book solution method
No Missing Variables ODE, Solve for \(y'\)

Mathematica
cpu = 0.0177357 (sec), leaf count = 47

\[\left \{\left \{y(x)\to c_1-\frac {2}{3} (1-x)^{3/2}-x\right \},\left \{y(x)\to c_1+\frac {2}{3} (1-x)^{3/2}-x\right \}\right \}\]

Maple
cpu = 0.022 (sec), leaf count = 35

\[ \left \{ y \relax (x ) =-x-{\frac {2}{3} \left (1-x \right ) ^{{\frac {3}{2}}}}+{\it \_C1},y \relax (x ) =-x+{\frac {2}{3} \left (1-x \right ) ^{{\frac {3}{2}}}}+{\it \_C1} \right \} \] 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),'implicit')

Maple raw output

y(x) = -x+2/3*(1-x)^(3/2)+_C1, y(x) = -x-2/3*(1-x)^(3/2)+_C1