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) + (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))
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]