##### 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 = 0.16033 (sec), leaf count = 59

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

Maple
cpu = 0.029 (sec), leaf count = 45

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

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

Mathematica raw output

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

Maple raw output

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