ODE
\[ y'(x)^2-(2 x+1) y'(x)-(1-x) x=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.027179 (sec), leaf count = 62
\[\left \{\left \{y(x)\to c_1+\frac {x^2}{2}+\frac {x}{2}-\frac {1}{24} (8 x+1)^{3/2}\right \},\left \{y(x)\to c_1+\frac {1}{2} \left (x^2+x+\frac {1}{12} (8 x+1)^{3/2}\right )\right \}\right \}\]
Maple ✓
cpu = 0.027 (sec), leaf count = 45
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}}{2}}+{\frac {x}{2}}-{\frac {1}{24} \left ( 8\,x+1 \right ) ^{{\frac {3}{2}}}}+{\it \_C1},y \left ( x \right ) ={\frac {{x}^{2}}{2}}+{\frac {x}{2}}+{\frac {1}{24} \left ( 8\,x+1 \right ) ^{{\frac {3}{2}}}}+{\it \_C1} \right \} \] Mathematica raw input
DSolve[-((1 - x)*x) - (1 + 2*x)*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x/2 + x^2/2 - (1 + 8*x)^(3/2)/24 + C[1]}, {y[x] -> (x + x^2 + (1 + 8*x)^(3/2)/12)/2 + C[1]}}
Maple raw input
dsolve(diff(y(x),x)^2-(1+2*x)*diff(y(x),x)-x*(1-x) = 0, y(x),'implicit')
Maple raw output
y(x) = 1/2*x^2+1/2*x-1/24*(8*x+1)^(3/2)+_C1, y(x) = 1/2*x^2+1/2*x+1/24*(8*x+1)^(3/2)+_C1