4.16.31 \(a y'(x)+b+y'(x)^2=0\)

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

[_quadrature]

Book solution method
Missing Variables ODE, Both independent and dependent variable missing

Mathematica
cpu = 0.00767415 (sec), leaf count = 53

\[\left \{\left \{y(x)\to c_1-\frac {1}{2} x \left (\sqrt {a^2-4 b}+a\right )\right \},\left \{y(x)\to \frac {1}{2} x \left (\sqrt {a^2-4 b}-a\right )+c_1\right \}\right \}\]

Maple
cpu = 0.02 (sec), leaf count = 43

\[ \left \{ y \relax (x ) =-{\frac {x}{2}\sqrt {{a}^{2}-4\,b}}-{\frac {ax}{2}}+{\it \_C1},y \relax (x ) ={\frac {x}{2}\sqrt {{a}^{2}-4\,b}}-{\frac {ax}{2}}+{\it \_C1} \right \} \] Mathematica raw input

DSolve[b + a*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> -((a + Sqrt[a^2 - 4*b])*x)/2 + C[1]}, {y[x] -> ((-a + Sqrt[a^2 - 4*b])
*x)/2 + C[1]}}

Maple raw input

dsolve(diff(y(x),x)^2+a*diff(y(x),x)+b = 0, y(x),'implicit')

Maple raw output

y(x) = -1/2*(a^2-4*b)^(1/2)*x-1/2*a*x+_C1, y(x) = 1/2*(a^2-4*b)^(1/2)*x-1/2*a*x+
_C1