##### 4.16.32 $$a y'(x)+b x+y'(x)^2=0$$

ODE
$a y'(x)+b x+y'(x)^2=0$ ODE Classiﬁcation

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for $$x$$

Mathematica
cpu = 0.182297 (sec), leaf count = 68

$\left \{\left \{y(x)\to -\frac {\left (a^2-4 b x\right )^{3/2}+6 a b x}{12 b}+c_1\right \},\left \{y(x)\to \frac {1}{2} \left (\frac {\left (a^2-4 b x\right )^{3/2}}{6 b}-a x\right )+c_1\right \}\right \}$

Maple
cpu = 0.033 (sec), leaf count = 49

$\left [y \left (x \right ) = -\frac {a x}{2}+\frac {\left (a^{2}-4 b x \right )^{\frac {3}{2}}}{12 b}+\textit {\_C1}, y \left (x \right ) = -\frac {a x}{2}-\frac {\left (a^{2}-4 b x \right )^{\frac {3}{2}}}{12 b}+\textit {\_C1}\right ]$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> -1/12*(6*a*b*x + (a^2 - 4*b*x)^(3/2))/b + C[1]}, {y[x] -> (-(a*x) + (a
^2 - 4*b*x)^(3/2)/(6*b))/2 + C[1]}}

Maple raw input

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

Maple raw output

[y(x) = -1/2*a*x+1/12*(a^2-4*b*x)^(3/2)/b+_C1, y(x) = -1/2*a*x-1/12*(a^2-4*b*x)^
(3/2)/b+_C1]