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 = 0.0499261 (sec), leaf count = 55

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

Maple
cpu = 0.048 (sec), leaf count = 49

\[ \left \{ x-{\frac {\ln \left (y \relax (x ) \right ) }{2}}-{\it Artanh} \left (\sqrt {1+4\,y \relax (x ) } \right ) -{\it \_C1}=0,x-{\frac {\ln \left (y \relax (x ) \right ) }{2}}+{\it Artanh} \left (\sqrt {1+4\,y \relax (x ) } \right ) -{\it \_C1}=0,y \relax (x ) =-{\frac {1}{4}} \right \} \] 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),'implicit')

Maple raw output

y(x) = -1/4, x-1/2*ln(y(x))+arctanh((1+4*y(x))^(1/2))-_C1 = 0, x-1/2*ln(y(x))-ar
ctanh((1+4*y(x))^(1/2))-_C1 = 0