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 = 0.0403969 (sec), leaf count = 68

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

Maple
cpu = 0.021 (sec), leaf count = 49

\[ \left \{ y \relax (x ) =-{\frac {ax}{2}}-{\frac {1}{12\,b} \left ({a}^{2}-4\,bx \right ) ^{{\frac {3}{2}}}}+{\it \_C1},y \relax (x ) =-{\frac {ax}{2}}+{\frac {1}{12\,b} \left ({a}^{2}-4\,bx \right ) ^{{\frac {3}{2}}}}+{\it \_C1} \right \} \] Mathematica raw input

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

Mathematica raw output

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

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