4.17.18 $$y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0$$

ODE
$y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0$ ODE Classiﬁcation

[_quadrature]

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

Mathematica
cpu = 0.238281 (sec), leaf count = 55

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

Maple
cpu = 4.193 (sec), leaf count = 193

$\left [y \left (x \right ) = -{\frac {1}{4}}, y \left (x \right ) = \frac {\left (\frac {{\mathrm e}^{-2 x} \textit {\_C1} \left (\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}-2\right )}{\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}}-{\mathrm e}^{-2 x} \textit {\_C1} -2\right ) {\mathrm e}^{2 x}}{2 \textit {\_C1}}, y \left (x \right ) = \frac {\left (\frac {{\mathrm e}^{-2 x} \textit {\_C1} \left (\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}+2\right )}{\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}}-{\mathrm e}^{-2 x} \textit {\_C1} -2\right ) {\mathrm e}^{2 x}}{2 \textit {\_C1}}, y \left (x \right ) = -\frac {\left (-\frac {{\mathrm e}^{-2 x} \textit {\_C1} \left (\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}+2\right )}{\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}}+{\mathrm e}^{-2 x} \textit {\_C1} +2\right ) {\mathrm e}^{2 x}}{2 \textit {\_C1}}, y \left (x \right ) = -\frac {\left (-\frac {{\mathrm e}^{-2 x} \textit {\_C1} \left (\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}-2\right )}{\sqrt {-{\mathrm e}^{-2 x} \textit {\_C1}}}+{\mathrm e}^{-2 x} \textit {\_C1} +2\right ) {\mathrm e}^{2 x}}{2 \textit {\_C1}}\right ]$ Mathematica raw input

DSolve[y[x]*(1 + 4*y[x]) - (1 + 4*y[x])*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> (E^(x - 4*C[1])*(E^x - 2*E^(2*C[1])))/4}, {y[x] -> (E^(x + 2*C[1])*(-2
 + E^(x + 2*C[1])))/4}}

Maple raw input

dsolve(diff(y(x),x)^2-(1+4*y(x))*diff(y(x),x)+(1+4*y(x))*y(x) = 0, y(x))

Maple raw output

[y(x) = -1/4, y(x) = 1/2*(1/exp(x)^2*_C1*((-1/exp(x)^2*_C1)^(1/2)-2)/(-1/exp(x)^
2*_C1)^(1/2)-1/exp(x)^2*_C1-2)*exp(x)^2/_C1, y(x) = 1/2*(1/exp(x)^2*_C1*((-1/exp
(x)^2*_C1)^(1/2)+2)/(-1/exp(x)^2*_C1)^(1/2)-1/exp(x)^2*_C1-2)*exp(x)^2/_C1, y(x)
 = -1/2*(-1/exp(x)^2*_C1*((-1/exp(x)^2*_C1)^(1/2)+2)/(-1/exp(x)^2*_C1)^(1/2)+1/e
xp(x)^2*_C1+2)*exp(x)^2/_C1, y(x) = -1/2*(-1/exp(x)^2*_C1*((-1/exp(x)^2*_C1)^(1/
2)-2)/(-1/exp(x)^2*_C1)^(1/2)+1/exp(x)^2*_C1+2)*exp(x)^2/_C1]