##### 4.17.38 $$2 y'(x)^2+2 (6 y(x)-1) y'(x)+3 y(x) (6 y(x)-1)=0$$

ODE
$2 y'(x)^2+2 (6 y(x)-1) y'(x)+3 y(x) (6 y(x)-1)=0$ ODE Classiﬁcation

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing, Solve for $$y'$$

Mathematica
cpu = 0.265622 (sec), leaf count = 69

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

Maple
cpu = 5.524 (sec), leaf count = 305

$\left [y \left (x \right ) = {\frac {1}{6}}, y \left (x \right ) = \frac {{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}} \left (-\sqrt {6}\, {\mathrm e}^{-\frac {3 x}{2}} {\mathrm e}^{\frac {3 \textit {\_C1}}{2}}+3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}\right )}{3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}-2}-2 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}-\frac {2 \left (-\sqrt {6}\, {\mathrm e}^{-\frac {3 x}{2}} {\mathrm e}^{\frac {3 \textit {\_C1}}{2}}+3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}\right )}{3 \left (3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}-2\right )}, y \left (x \right ) = \frac {{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}} \left (\sqrt {6}\, {\mathrm e}^{-\frac {3 x}{2}} {\mathrm e}^{\frac {3 \textit {\_C1}}{2}}+3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}\right )}{3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}-2}-2 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}-\frac {2 \left (\sqrt {6}\, {\mathrm e}^{-\frac {3 x}{2}} {\mathrm e}^{\frac {3 \textit {\_C1}}{2}}+3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}\right )}{3 \left (3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}-2\right )}, y \left (x \right ) = -\frac {{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}} \left (\sqrt {6}\, {\mathrm e}^{-\frac {3 x}{2}} {\mathrm e}^{\frac {3 \textit {\_C1}}{2}}-3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}\right )}{3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}-2}-2 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}+\frac {\frac {2 \sqrt {6}\, {\mathrm e}^{-\frac {3 x}{2}} {\mathrm e}^{\frac {3 \textit {\_C1}}{2}}}{3}-2 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}}{3 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 \textit {\_C1}}-2}\right ]$ Mathematica raw input

DSolve[3*y[x]*(-1 + 6*y[x]) + 2*(-1 + 6*y[x])*y'[x] + 2*y'[x]^2 == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(2*diff(y(x),x)^2+2*(6*y(x)-1)*diff(y(x),x)+3*y(x)*(6*y(x)-1) = 0, y(x))

Maple raw output

[y(x) = 1/6, y(x) = 1/exp(x)^3*exp(_C1)^3*(-6^(1/2)*exp(-3/2*x)*exp(3/2*_C1)+3/e
xp(x)^3*exp(_C1)^3)/(3/exp(x)^3*exp(_C1)^3-2)-2/exp(x)^3*exp(_C1)^3-2/3*(-6^(1/2
)*exp(-3/2*x)*exp(3/2*_C1)+3/exp(x)^3*exp(_C1)^3)/(3/exp(x)^3*exp(_C1)^3-2), y(x
) = 1/exp(x)^3*exp(_C1)^3*(6^(1/2)*exp(-3/2*x)*exp(3/2*_C1)+3/exp(x)^3*exp(_C1)^
3)/(3/exp(x)^3*exp(_C1)^3-2)-2/exp(x)^3*exp(_C1)^3-2/3*(6^(1/2)*exp(-3/2*x)*exp(
3/2*_C1)+3/exp(x)^3*exp(_C1)^3)/(3/exp(x)^3*exp(_C1)^3-2), y(x) = -1/exp(x)^3*ex
p(_C1)^3*(6^(1/2)*exp(-3/2*x)*exp(3/2*_C1)-3/exp(x)^3*exp(_C1)^3)/(3/exp(x)^3*ex
p(_C1)^3-2)-2/exp(x)^3*exp(_C1)^3+2/3*(6^(1/2)*exp(-3/2*x)*exp(3/2*_C1)-3/exp(x)
^3*exp(_C1)^3)/(3/exp(x)^3*exp(_C1)^3-2)]